Evaluating the 'Leverage Theory' of Product Bundling in the by kzl15411

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									                              CMPO Working Paper Series No. 00/22




     Evaluating the 'Leverage Theory' of Product
       Bundling in the Context of Negotiations

                                           Esther Gal-Or

                 Katz Graduate School of Business, University of Pittsburg



                                            January 2000


Abstract
I have developed a model to evaluate the leverage theory of product bundling in the context of
negotiations between a monopolist and intermediaries who sell its products to consumers. I
investigated whether the monopolist finds it feasible and advantageous to utilize product bundling in
order to block negotiations between the intermediaries and a rival firm who competes against the
monopolist in a complementary market. My results support the Chicago School conventional wisdom
that product bundling is ineffective in extending monopoly power, even in this modified environment
where it affects the bargaining position of the monopolist in negotiations with powerful business
partners. Specifically, the monopolist finds foreclosure of competitors via bundling either unprofitable
or not feasible.


Acknowledgements
This work was supported by the National Science Foundation under grant SBR-981-
9373. This research falls under the Regulation of Newly Privatised Entities
programme funded by the Leverhulme Trust.

Address for Correspondence
Esther Gal-Or
210 Mervis Hall
Katz Graduate School of Business
University of Pittsburgh
Pittsburgh
PA 15260
USA
esther@mail.business.pitt.edu




                               CMPO is funded by the Leverhulme Trust.
1. Introduction
                    o h e e       h                   ing   ie                       h        e
        A ccording t t e lv rage t e ory, product bundl is v w ed as a m e ch anism t at e nabls
           h       y                           o e e     h                      o      ose e
a firm w it m onopol pow e r in one m ark e t t lv rage t is pow e r in orde r t fore cl sals and
 h              ize                   .
t e reby m onopol a s e cond m ark e t Th e Ch icago Sch ool ic of th e t
                                                            crit         radit     l e        h
                                                                              ional e v rage t e ory
t     ly           h
 ypical assum e s t at t e s e cond m ark e t is perfe ct y com pet iv . Th e m onopol is unabl
                        h                                l         it e              ist      e,
 h             o
t e re fore , t e xt         us      h                    ,                                      osure
                    ract surpl from t e s e cond m ark e t and h e nce cannot benefit from fore cl
 h          ing              or    e i
t rough bundl (s e e D ire ct and L v (19 56), Bow m an (19 57), Posner (19 67), and Bork
                           osure t e ory" al s for im pe rfe ct com pe t ion in t e s e cond m ark e t (s e e
(19 78).) Th e "ne w fore cl      h        low                          it       h
               ton                      e                   on                             -al
A gh ion and Bol (19 87), H art and Tirol (19 9 0), W h inst (19 9 0), and R asm us e n e t (19 9 1).)
           rat h         h                          it
It dem onst e s t at w it such im pe rfe ct com pe t ion, circum stance s m ay aris e unde r w h ich a
       ist     il       ing       e
m onopol can ut ize bundl of com plm e nt product in orde r t pre s e rv and e xt nd it
                                         ary     s           o          e        e     s
       y
m onopol posit                ying assum pt of th e "ne w t e ory" as w e l as of product bundl
              ion. Th e unde rl            ion             h              l                   ing
                       ion  ice igl                        le                  e
as a price discrim inat de v (St e r (19 68), Adam s and Yel n (19 76), Sch m alns e e
                                    lan           on                    h h            ist l ss
(19 82,19 84) and M cA fe e , M cM il and W h inst (19 84),) h as been t at t e m onopol s e l it
       s      l o         ess,     ak                        e                     s
product direct y t pow e rl price t ing consum e rs. H ow e v r, in m any m ark e t w h e re
    ing              al                            y lh                s o       ess
bundl h as been pre v e nt firm s do not ne cessaril sel t e ir product t pow e rl consum e rs.
            e                   s   ude h                  ry                            ed e
Tw o e xam pls of such m ark e t incl t e s oftw are indust w h e re M icrosoft h as bundl Int rne t
   ore                               th              s             ing     ak    h
Expl r as part of W indow s and h e al care m ark e t w h e re bundl h as t e n t e form of
         ion
acq uisit of ph ysician pract               al
                             ices by h ospit s.
            h      t            ry,
        In t e s of w are indust M icrosoft rare l sel it operat syst m dire ct y t consum e rs.
                                                 y l ss         ing  e         l o
                   e
Be caus e of th e t ch nical       tie        aling h                                              e
                            difficul s of inst l t e softw are , m ost consum e rs e xpe ct com put r
         ure o l h                          h h         ing  e
m anufact rs t s e l t e ir m ach ine s w it t e ope rat syst m al ady inst l As a re s ul
                                                                 re        aled.         t,
                 o      iat ice                 s    h       e           ure             e
M icrosoft h as t ne got e l nsing agre e m e nt w it com put r m anufact rs w h o s e rv as
   e               w       h                                                     ure      urn
int rm ediaries bet e e n t e s oftw are giant and consum e rs. Th os e m anufact rs, in t are not
          y        ess,     ak       it           ude                                       l
ne cessaril pow e rl price t ing e nt ie s and incl com panies such as Com paq , IBM or D e l.
             arl          th              s e           al h
        Sim il y, in h e al care m ark e t e v n h ospit s w it significant m ark e t pow e r do not
           ie s      l       h        ice h
ch arge pat nt direct y for t e s e rv s t ey prov . Inst ad t ey h av t ne got e t rm s of
                                                  ide    e    h       e o      iat e
                        h arge and pow e rful e al insurers and H M O 's. To t s t t e lv rage t e ory in
re im burs e m e nt w it l                   h t  h                           e h e e           h
 h      e               e      e              h                                ist     iat e
t e cont xt of th e abov exam pls or in any ot e r m ark e t w h e re a m onopol ne got e s t rm s of
t         h          cust                   ant o  icit y  ure h      iat
 rade w it pow e rful om e rs, it is im port t e xpl l capt t e ne got ions process in


                                                      1
        o      ify h                ion                   ie    oled. In t e pre s e nt pape r I
orde r t ide nt t e bargaining posit of e ach of th e part s inv v        h
   e op            iat               t
dev l such a ne got ion based m ode l o inv s t e w h e t e r a m onopol can e xt nd it
                                           e igat        h             ist       e     s
       y      ion ia         ing
m onopol posit v product bundl w h e n it s e l it product indire ct y t consum e rs t rough
                                              l s
                                               s          s         l o               h
   e
int rm ediarie s .
                      a       ist                                                e              h
        In m y m ode l m onopol (Firm 1) in one m ark e t (M ark e t A ) com pe t s against anot e r
                        e      ary                                    ing     s
firm (Firm 2) in a com plm e nt m ark e t (M ark e t B). Th e com pe t product in M ark e t B are
         ed o             iat                                 at h       h         s
pe rce iv t be diffe re nt ed by consum e rs. Efficie ncy dict e s t at t e product of th e
       ist     s        it         d h          e                    so
m onopol and it com pe t or are s ol t rough int rm ediarie s w h o al possess som e m ark e t
               ure h                       h h              y w      e
pow e r. I capt t is pow e r by assum ing t at t e re are onl t o int rm ediarie s w h o are
             o              iat       h           iv                          e                 iat
conside red t be diffe re nt ed from t e pe rspect e of consum e rs. Th e e xt nt of diffe re nt ion
bet e e n t e int rm ediaries det rm ine s t e s t ngt of th e ir ne got ing posit v
   w       h     e               e          h     re h                  iat                 Ρs h
                                                                                  ion is-a-v t e firm s.
          ysis, I inv s t e w h e t e r by bundl it product t t e r t e m onopol can bl
In m y anal          e igat        h           ing s       s oge h   h         ist    ock
 h        iat      w
t e ne got ions bet e e n t e int rm ediarie s and Firm 2 and by doing so, lv rage it m onopol
                           h     e                                         e e       s       y
     ion                o                       ts         h
posit from M ark e t A t M ark e t B. M y re s ul support t e Ch icago Sch ool    e ional
                                                                              conv nt
         h               ing            e               dev         e             y
w isdom t at product bundl cannot s e rv as a successful ice in e xt nding m onopol pow e r.
          ly,        h
Spe cifical w h e n t e m ark e t is com plt y cov red so t at t e e nt popul ion of consum e rs
                                          e el    e        h h         ire  at
part      e                   h
    icipat in it and w h e n t e degre e of diffe re nt ion be t e e n t e int rm ediarie s is re l iv l
                                                       iat      w       h     e                   at e y
    l h
     ,           ist
sm al t e m onopol ne v r finds it profit e t bundl it product t t e r in orde r t bl t e
                       e                 abl o    e s         s oge h             o ock h
      iat       h s         it                  h     e                     e e       y
ne got ions w it it com pe t or, Firm 2. Since t e int rm ediarie s com pe t int ns e l for
                h          h         ist
consum e rs in t is cas e t e m onopol can ut ize it m onopol posit in M ark e t A t e xt
                                             il s           y      ion              o    ract a
arge s h are of th e s urpl generat in t e ne got ions w it t e int rm ediarie s . Th is surpl is
l                         us       ed   h        iat       h h     e                         us
               urn                 e h           o          h                      h h
h igh e r, in t if consum e rs h av t e freedom t ch oos e t e brand of product B t at t ey prefe r
    .
best Sabot       h        iat
          aging t e ne got ions bet e e n Firm 2 and t e int rm ediarie s is count rproduct e
                                   w                  h     e                     e        iv
 h                  h           iv     h         ist                                   at
t e re fore , from t e pe rspect e of t e m onopol . W h e n a s e gm e nt of th e popul ion of
                                    ion          h                        iat      w       h
consum e rs re frains from consum pt or w h e n t e degre e of diffe re nt ion be t e e n t e
   e                   at e y                  e
int rm ediarie s is re l iv l h igh , e ach int rm ediary h as a st                        ion  h
                                                                   ronge r bargaining posit in t e
      iat       h h         ist     h                                  us              o h
ne got ions w it t e m onopol . W it a significant sh are of th e s urpl now accruing t t e
   e                 h        iat                        iv o
int rm ediarie s in t e ne got ion, e ach h as an ince nt e t incre as e t e w il
                                                                          h     l         o
                                                                                 ingness t pay of its
    om
cust e rs. Prov          om                               h
               iding cust e rs freedom of ch oice am ong t e brands of product B incre ases
         h      l
indeed, t is w il         o
                 ingness t pay. H e nce, ev n w h e n t e m onopol bundls it t o product
                                           e           h         ist   e s w            s


                                                      2
 oge h   h     e
t t e r t e int rm ediaries st l
                              il find it opt al o re ach an agre e m e nt w it Firm 2 as w e l Giv n
                                            im t                              h              l.   e
 h         osure v bundl is e it e r unprofit e t t e m onopol or not fe asibl, t e pre s e nt
t at fore cl      ia   ing      h            abl o h         ist             e h
       t       o         h ie h                  ing          e          y
m ode l e nds t support t e v w t at product bundl cannot e xt nd m onopol pow e r.
                        ure             yie d h                  t       h
        Tw o m ain fe at s of m y m odel l t e diffe re nt re s ul from t at obt          h
                                                                                ained in t e "ne w
e e      h             , h
lv rage t e ory". First t e assum pt t at t e m onopol and it com pet or produce
                                    ion h  h         ist     s       it
           iat           h                         ie h      h                          ot surpl (or
diffe re nt ed goods in t e s e cond m ark e t im pl s t at t e re is an incre as e in t al    us
                            w                                        e     h                    .
e fficie ncy gain) if th e t o diffe re nt brands are offe red for sal in t e s e cond m ark e t Se cond,
         h               d h          e              h         ist
w h e n t e goods are s ol t rough int rm ediarie s t e m onopol can e xt                       ion
                                                                         ract a significant port of
 h             us      h     e                          s            h         y
t is added surpl from t e int rm ediaries becaus e of it pow e r in t e m onopol good. Th e
       ist                   iv      h
m onopol h as reduced ince nt e s , t e re fore t pre v nt t e int rm ediarie s from deal w it it
                                                 o     e h        e                     ing   h s
        it      h                    .
com pe t or in t e s e cond m ark e t In cont , w h e n t e goods are s ol dire ct y t final
                                             rast        h               d        l o       consum e rs,
                   h        ing it ure h                                   h         ist o
as is assum ed in t e e xist l e rat , t e re is no such m e ch anism for t e m onopol t e xtract
 h            us       ed   h
t e added surpl generat in t e s e cond m ark e t and fore cl
                                                 ,                              e            t
                                                            osure can be desirabl as a re s ul.
        Th e m ain cont     ion                    ysis
                       ribut of th e pre s e nt anal is in ident                 ant
                                                                ifying an im port circum stance
                  ist            abl    e s              h                      o    ude s   al
w h e re a m onopol cannot profit y bundl it product w it a s e cond m ark e t t e xcl it riv s
 h          h     h
t e re . I t ink t is cont     ion
                          ribut is im port for at last t o re asons. First from a t e ore t
                                          ant     e     w                 ,        h       ical
         iv h       arifie s t e rol of ne got ions w it int rm ediarie s in re v rsing t e lv rage
pe rspect e , t is cl         h    e          iat       h   e                    e       h e e
 h                                  ing                   lh              s h         e
t e ory. Se cond, since product bundl by firm s w h o s e l t e ir product t rough int rm ediarie s
           ted                 i-t               h               h              e           icy
h as re s ul in significant ant rust conce rns, t e findings in t is pape r h av profound pol
    icat
im pl ions.
             h                    e             at h           in h     e                   m
        For t e s ak e of concre t ness I form ul e t e m ode l t e cont xt of th e D e part e nt of
 ust                                          it                          e                 h       e
J ice 's cas e against M icrosoft. Th e ide nt ie s of th e firm s and int rm ediarie s in t is cont xt are
M icrosoft, Ne t             h         e
                scape , and t e com put r m anufact rs, w h o w h e n s e l t e ir com put rs bundl
                                                   ure                     ing
                                                                          l h             e       ed
    h h         ing  e        e      e               w       h
w it t e ope rat syst m s e rv as int rm ediaries bet e e n t e s oftw are produce rs and consum e rs.
         s             h       e
M ark e t A and B, in t is cont xt are t e ope rat syst m s and brow s e rs m ark e t re s pe ct e l
                                        h         ing  e                             s,         iv y.
     e               h e e       h                     ing at           l o
W h il m y focus on t e lv rage t e ory of product bundl re l es dire ct y t som e of th e
accusat              ust          m                                    can   y    im ed
       ions of th e J ice D e part e nt against M icrosoft, m y m ode l be onl of l it use in
 h       e .           ly,
t is cont xt Spe cifical it doe s not address a m aj com pl of th e D e part e nt of J ice t at
                                                    or    aint              m         ust   h
      osing t e brow s e rs m ark e t m ay h av act l been int nded t prot ct M icrosoft's m onopol
fore cl      h                                 e   ualy       e      o    e                       y
     ion  h         ing  e
posit in t e ope rat syst m s m ark e t (by pre v nt t e dist
                                                 e ing h          ion       e    J a
                                                             ribut of a Univ rsal av


                                                      3
    e                         t           ist     e h       e                                      h
Syst m ). Since in m y m ode l h e m onopol is nev r t re at ned in M ark e t A, I cannot address t is
      e     iv ion                  osure. H ow e v r, re ce nt t e ore t
possibl m ot at for m ark e t fore cl              e             h       icalfindings (Ch e n (19 9 8))
        rat    o     ik y h                            e     ed o     os h
dem onst e it t be unl e l t at M icrosoft m igh t h av w ant t fore cl e t e Brow s e rs m ark e t in
        o    e     s       y
orde r t prot ct it m onopol posit in t e syst m s m ark e t According t t e pape r, w h e n goods
                                  ion  h      e             .           o h
       rat         e      s,        ist          ry h        l       h
are s t e gic com plm e nt a m onopol facing e nt t re at w il w in t e bidding for a ne w m ark e t
           e      h
anyw ay, ev n in t e absence of bundl
                                    ing. M ore ov r, if due t t ch nical
                                                 e           o e                          h
                                                                        deficie ncie s , t e future
        s            e    J a     e                              iv
prospect of th e Univ rsal av Syst m w e re in doubt irre s pe ct e of th e act      ak
                                                                               ions t e n by
                     l re
M icrosoft (s e e W al St e t J      art e                                 h      l
                               ournal icls on 12/4/9 8, and 2/1/9 9 or in t e Port and O re gonian on
            h
12/4/9 8), t e n Ne t                        e
                     scape 's brow s e r ne v r re al posed any s e rious t re at t M icrosoft's m onopol
                                                    ly                     h       o                    y
     ion  h         ing  e
posit in t e ope rat syst m s m ark e t Th e re s ul of th e pre s e nt anal t nd t support
                                       .           ts                      ysis e  o       ,
 h                             e ion h      ing e          ore
t e re fore , M icrosoft's cont nt t at bundl Int rne t Expl r as part of W indow s h as been
    iv ed                 e                         h        osure of Ne t
m ot at by enh ancing conv nie nce of us e and not t e fore cl                        h
                                                                          scape from t e m ark e t.
            e     ing       icabil y t t e D e part e nt of J ice cas e against M icrosoft, I do
       W h il h av som e appl    it o h            m         ust
               h        ure o  h
not conside r t is fe at t be t e m ain contribut of th e pre s e nt anal
                                                 ion                    ysis. R at e r, t e pape r
                                                                                  h      h
  t      s o al e               t e e         h                     ing   h      e
at e m pt t e v uat in ge ne ral h e lv rage t e ory of product bundl in t e cont xt of
      iat
ne got ions am ong pow e rful             ne          h         e        ry h         ne
                             business part rs. If in t e com put r indust t e s e part rs are
                                e           ure          th              s h        iat      ne
softw are produce rs and com put r m anufact rs, in h e al care m ark e t t e ne got ing part rs
           al                          ts          ysis y o h at e           e        l
are h ospit s and insurers. Th e re s ul of m y anal appl t t e l t r e xam pl as w e l since in
             al        s,
m any h ospit m ark e t w h e re v rt
                                  e ical e rge rs bet e e n h ospit s and ph ysician pract s h av
                                        m            w             al                     ice    e
 ak    ace h                    al                                       o ocal      y
t e n pl , t e m e rging h ospit h ad significant m ark e t pow e r due t a l m onopol
     e y         t               Ce e            e          v
(Univ rsit of Pit sburgh M edical nt r in w e s t rn Pe nnsylania, for instance ). A conce rn h as
                o       h           ing s    ice    h h                                    h
been raised as t w h e t e r by bundl it serv s w it t os e of th e acq uired ph ysicians t e
       al t      s o    e     s
h ospit at e m pt t e xt nd it m onopol posit t t e ph ysicians m ark e t as w e l Th e e xist
                                      y      ion o h                             l.           ing
it ure      h e e       h                al e h                      ey             s o     ure h
l e rat on t e lv rage t e ory cannot e v uat t is conce rn ade q uat l since it fail t capt t e
      iat             w             al                          iat              t           e op
ne got ion process bet e e n h ospit s and insurers. Th e ne got ion based m odel h at I de v l
           e    e o                    al ion.
offe rs a v h icl t conduct such an e v uat
                                     low A                    h
       Th e pape r is organized as fol s; fte r de s cribing t e assum pt                    in h
                                                                         ions of th e m ode l t e
            ion
ne xt s e ct I distinguish in Se ct                 w
                                   ions 3 and 4 be t e e n t e cas e t at al consum e rs are act e in t e
                                                            h         h    l                    iv     h
               h         h                             at
m ark e t and t e cas e t at a s e gm e nt of th e popul ion re frains from consum pt          ion
                                                                                     ion. Se ct 5
    ude h
concl s t e pape r.


                                                    4
2. Th e M od e l
                   w             s              h       e o                                e
        Conside r t o com pone nt of softw are t at h av t be used by consum e rs as a syst m , say
 h         ing  e       h
t e ope rat syst m and t e w eb brow s e r. W h il a singl firm produce s t e ope rat syst m
                                                 e       e                 h         ing  e
                                        ing
(M icrosoft) tw o firm s offe r com pe t w eb brow s e rs (Ne t                              e
                                                               scape and M icrosoft.) Com put r
         ure     e o    al t     y ail e
m anufact rs h av t inst l h e onl av abl ope rat syst m in conj
                                                 ing  e             ion  h
                                                                unct w it a w eb
                  o l h ing            e o       om                  w                ure     h
brow s e r prior t s e l t e ir com put rs t cust e rs. Th e re are t o such m anufact rs in t e
                 l
m ark e t (say Del and Com paq .)

                               h w                            l h             e
        Consum e rs conside r t e t o w eb brow s e rs as w e l as t e com put rs produced by diffe re nt
         ure               iat        s.      ure h            iat              h h ide
m anufact rs as diffe re nt ed product To capt t is diffe re nt ion, I assum e t at t e “ al
     s” h        at                       h            o h                               y
point of t e popul ion of consum e rs w it re s pe ct t t e w eb brow s e rs are uniform l distributed
     ine           e h      h h w          ing               ocat     h           s
on a l of one unit lngt w it t e t o e xist w eb brow s e rs l ed at t e e ndpoint of th is
ine
l . Each consum e r incurs t        at       s       t
                            ransport ion cost e q ual o t2 pe r unit of distance w h e n purch asing a

                ocat      e          s        e ics             h            s ide point
w eb-brow s e r l ed, in t rm s of it ch aract rist aw ay from t e consum e r’“ al      .”
     arl h                        h            o
Sim il y, t e pre fe re nce s w it re s pe ct t com put rs are al represent by a uniform dist
                                                       e        so         ed                ribution
    ide point on a l of one unit lngt w it t e t o m anufact rs l ed at t e e nd point
of “ al      s”    ine           e h      h h w             ure ocat     h            s
         ine
of th is l . Th e t        at
                   ransport ion param e t r de s cribing t is dist
                                         e                h            ion         ed
                                                                  ribut is designat by t1 . H e nce ,

                      h      e                 iat      w                            h         e
 t2 and t1 m e asure t e e xt nt of diffe re nt ion be t e e n w eb-brow s e rs and t e com put rs of
                     ure            iv y.           h h
diffe re nt m anufact rs, re s pe ct e l I assum e t at t e dist     ion                   w
                                                                ribut of pre fe re nces bet e e n w eb-
                  e
brow s e rs is det rm ined inde pe nde nt of th e dist     ion                   w       h w
                                                      ribut of pre fe re nces bet e e n t e t o
m anufact rs. I de s ignat by x t e dist
         ure              e      h                                    h           ure ocat
                                        ance of th e consum e r from t e m anufact r l ed at
 h e
t e lft e nd point of th e dist     ion                                 ure
                               ribut of pre fe re nce s am ong m anufact rs, and by y h e r distance

      h                  ocat     h e
from t e w eb brow s e r l ed at t e lft e nd point of th e dist     ion
                                                                ribut am ong brow s e rs. I assum e
 h             s e           ore
t at M icrosoft’Int rne t Expl r is l ed at t e l and Net
                                    ocat     h eft                igat    h
                                                         scape Nav or at t e righ t e nd
     s
point of th is distribut                                h         e       h
                        ion. W h e n a consum e r uses t e com put r and t e w eb-brow s e r w h os e
        e ics       l      ch
ch aract rist e xact y m at h e r “ al
                                   ide point sh e deriv s ut it equal o v , w h ich can be
                                            ”          e    il y     t
int rpre t as h e r re s e rv ion price . Th is lv l ut it decl s t (v - t1 x − t 2 y ) w h e n a
   e      ed                 at                 e e of il y   ine o
                              h         e                      ocat     h e
consum e r of type x, y buys t e com put r and w eb-brow s e r l ed at t e lft e nd point of th e

corre s ponding distribution.



                                                      5
                  h                        h    h
       I assum e t at consum e rs prefe r t at t e com put r m anufact r inst l t e ope rat
                                                          e           ure      s
                                                                             al h          ing
    e       h                         h                 e
syst m and t e w eb brow s e r since t ey expe rie nce t ch nicaldifficul s in inst l t ose syst m s
                                                                        tie        aling h      e
 h        v              e h                               e
t e m s e le s . M ore ov r, t ey expe rie nce m uch gre at r difficul s in inst l t e ope rat syst m
                                                                     tie        aling h       ing  e
 h          aling h                           l
t an in inst l t e w eb brow s e r. Spe cifical w h il t ey are unabl t inst l h e ope rat
                                               y,    e h            e o     al t          ing
    e         t h                        , h
syst m no m at e r t e re s ources spe nt t ey can inst l brow s e r at an addit
                                                       al a                     ional            l
                                                                                     cost of k dolars
         h       e e incurred by t e m anufact r.)
(beyond t e cost lv l             h           ure

              e h                     ure       ow        s       alat    h
       It is clar t at since m anufact rs incur l e r cost of inst l ion t an consum e rs,
                 at h                                lh           e     h             e           ure
e fficie ncy dict e s t at softw are com panie s s e l t e ir syst m s t rough com put r m anufact rs
   h     h          l o
rat e r t an dire ct y t consum e rs. H ow e v r, since m y obj ct e in t e pape r is t assess t e
                                              e                e iv      h             o        h
       it h h              ist              s       y      ion                o    ude s
possibil y t at t e m onopol ic firm uses it m onopol posit in one m ark e t t e xcl it
        it        h       em
com pe t or from t e com pl e nt brow s e rs m ark e t by bundl it product t t e r, I al for
                                ary                           ing s       s oge h      low
 h         it h
t e possibil y t at Ne t                o ls                        l o                           e
                        scape ch ooses t s e l it brow s e r dire ct y t consum e rs. I de s ignat by p N

 h         h
t e price t at Ne t                                     h                        at           e     h
                   scape ch arge s from consum e rs in t at cas e . Such a form ul ion guarant e s t at
Ne t               e   iabl
    scape m ay h av a v e "outside opt        e                                                h h
                                      ion" e v n w h e n it cannot re ach an agre e m e nt w it t e
         ure
m anufact rs.

                                      ly            h                    l
       Since consum e rs do not norm al purch as e t e s oftw are dire ct y from M icrosoft and
Ne t                 ure     e o      iat    h                      e                  ice
    scape , m anufact rs h av t ne got e w it softw are produce rs t rm s of trade for l nsing
t e ir t ch nol s . As a re s ul of such ne got ions, com put r m anufact r i agre e s t pay
 h      e     ogie             t               iat           e           ure            o
                        alat               aling     ee     e                    h
M icrosoft rTi pe r inst l ion w h e n inst l a com plt syst m com prising of bot W indow s and

   e         ore            e ot syst       e              e h         o         o
Int rne t Expl r (T designat s t al e m ). L t rwi designat t e price t be paid t M icrosoft

            aling y s
w h e n inst l onl it operat syst m ( w designat s W indow s onl Sim il y, lt rN
                            ing  e              e              y.)    arl e i

        e h        iat          w
designat t e ne got ed price bet e e n produce r i and Ne t               h
                                                           scape w h e n t e w eb brow s e r of ch oice
 h          aled
t at is inst l is Netscape ’Nav or. I de s ignat by p si t e price ch arged from consum e rs by
                           s   igat             e         h

         ure              ling            e                    h h                  h
m anufact r i w h e n s e l a ne w com put r com prising of bot t e h ardw are and t e s oftw are
    al
inst led.

           h                       rict                           h           ure
       In t e absence of any re s t ions im posed by M icrosoft, t e m anufact r is fre e to
                   s      ing  e      h
com bine M icrosoft’operat syst m w it Ne t      s                                    ed
                                           scape ’w eb brow s e r, w h e n re q ue s t by
                              e    e     e
consum e rs. If M icrosoft int grat s Int rne t Expl r int it ope rat syst m m anufact rs are
                                                   ore    o s        ing  e           ure


                                                     6
        o    al Expl r as t e w eb brow s e r re gardls s of th e pre fe re nce s of consum e rs. As
forced t inst l    ore     h                         e
     ed       ie
point out e arl r, Ne t            il t o l s                      l o                  h
                       scape can st l ry t s e l it product dire ct y t consum e rs in t at cas e .

         icit            h    l                                 l                         y
For sim pl y, I assum e t at al produce rs (of softw are as w e l as h ardw are ) incur onl fixed cost
of product 1
          ion.

                  t                    ing        age      h          age         ure      iat
         I m ode l h e gam e as consist of tw o st s . At t e first st , m anufact rs negot e
    h
w it M icrosoft and Ne t               tane y              o
                        scape and sim ul ousl set price s t be ch arged from consum e rs. I
         h           e           ure   s o                             h                       h
assum e t at if a giv n m anufact r fail t re ach an agre e m e nt w it a softw are produce r t e
    ie         e           iat
part s can ne v r re ne got e in t e fut . In addit
                                  h     ure                            ure             e h
                                                   ion, e ach m anufact r cannot observ t e
out          h        iat        s
   com e of t e ne got ions of it com pe t ors. Th e assum pt
                                          it                      h       h          age    iat
                                                             ion t at in t e first st ne got ions
 ak  ace     tane y
t e pl s im ul ousl w it price s e t ing can be re pl
                        h           t                        h             ial  e ype of gam e ,
                                                    aced w it a s e q ue nt m ov t
               iat                    t        ong       e         e           ure
w h e re ne got ions precede price set ing. As l as a giv n com put r m anufact r cannot
      e h e                             s        it h          tane                 ial
observ t e t rm s of trade secured by it com pe t or t e s im ul ous and s e q ue nt m ove
              s   d
arrange m e nt yiel ident    re t
                         ical s ul In t e s e cond st of th e gam e Net
                                  s.   h             age                                    h
                                                                       scape decides w h e t e r to
s e l it product dire ct y t consum e rs and unde r w h at t rm s.2
    ls                  l o                                 e

                   t          iat      w             e           ure
         To m ode l h e ne got ions bet e e n com put r m anufact rs and softw are produce rs I us e
 h                    ut            h
t e Nash Bargaining Sol ion. Using t is coope rat e s ol ion conce pt t m ode l h e bil e ral
                                                 iv    ut              o       t      at
      iat      w           e           ure         e
ne got ions bet e e n a giv n m anufact r and a giv n softw are produce r doe s not proh ibit m e
from capt       h         it h                     it                 w       h w             ure
         uring t e possibil y t at fie rce com pe t ion m ay exist bet e e n t e t o m anufact rs or
   w       h w                            e ed,
bet e e n t e t o w eb brow s e rs as re flct for inst           h al                       e
                                                      ance , by t e v ue s of th e param e t rs t1 and

            h                    ut              ed
t2 . Since t e Nash Bargaining Sol ion is com put by ident                h           o h
                                                          ifying payoffs t at accrue t t e

      iat      ies h
ne got ing part bot in cas e of agre e m e nt as w e l as disagre e m e nt bet e e n t e m , t e ext nt of
                                                     l                        w       h       h     e
        it       h                       s      t o          cul ions. For inst
com pe t ion in t e diffe re nt m ark e t is buil int such cal at              ance , reduced
           iat      w       h w                            e ed         l al
                                                                         e                 ie h h
diffe re nt ion be t e e n t e t o w eb brow s e rs as re flct by a sm al r v ue of t2 im pl s t at t e

 out
“ side opt            e
          ion”of a giv n m anufact r is m ore fav
                                  ure                e                                  h
                                                 orabl in cas e of disagre e m e nt w it Ne tscape .



1
                     ion         al o             ant
  Such an assum pt is e q uiv e nt t a const pe r unit v         ariabl cost Al of th e q ual at e re s ul rem ain unch anged
                                                                       e      .  l           it iv         ts
    h              iv
w it such a posit e pe r unit v          e
                                  ariabl cost e v n w h en t ose v
                                              , e              h           e    s ary                    irm
                                                                     ariabl cost v across diffe re nt f s.
2
      e h                            h           it h                       so l        l o
  Ev n t ough I do not consider t e possibil y t at M icrosoft can al sel dire ct y t consum e rs it is easy t    o
           rat h h          ion        e        abl
dem onst e t at t is opt is nev r profit e for M icrosoft giv it m onopol posit in t e ope rat syst s
                                                                        en s          y     ion    h          ing    em
               h        h                                   alat         h            ure
m ark e t and t e fact t at consum e rs incur h igh e r inst l ion cost t an m anufact rs.


                                                              7
  s                ion is-à is
It bargaining posit v -v Net               d
                               scape s h oul be stronge r, t e re fore , t us t
                                                            h             h        at     o ow
                                                                               ransl ing t a l e r
      iat           ice
ne got ed price for l nsing Ne t      s e     ogy.
                                scape ’t ch nol

             v                                ibria I st by conside ring t e s e cond st w h e n
        To sole for sub-gam e pe rfe ct e q uil         art               h             age
Ne t                     h     o         s                  l o                      e h
    scape decides w h e t e r t offe r it brow s e r dire ct y t consum e rs. It is clar t at such an
   ion        t iv
opt m ay be at ract e if Ne t         d                                 h   e
                             scape coul not re ach an agre e m e nt w it at last one of th e
m anufact rs.3 In cas e of disagre e m e nt bet e e n Ne t
         ure                                   w          scape and a giv n m anufact r i , Int rne t
                                                                         e           ure       e
   ore        aled    e
Expl r is inst l on ev ry com put r sol by t is m anufact r re gardls s of th e pre fe re nce s of
                                 e    d     h            ure       e
 h
t e consum e r. If Ne t          l s
                                  s            o                ure         om
                       scape s e l it product t one of m anufact r i' s cust e rs as a s e cond
             h       om         o
brow s e r, t is cust e r h as t inst l h e brow s e r h e rs e l O nl if th e cust e r h as a st
                                     al t                       f.   y             om            rong
                   h     igat   l                        h                                  s
pre fe re nce for t e Nav or w il sh e conside r buying t e s e cond brow s e r w h ich cost h e r an e xtra
price of ( p N + k ) incl e of th e cost of inst l ion. Spe cifical lt m anufact r i be t e one
                        usiv                    alat               y,
                                                                  l e           ure      h

ocat     h eft
l ed at t e l e nd point of th e distribut of pre fe re nces bet e e n m anufact rs, t e n al
                                          ion                   w               ure   h     l
consum e rs of type y sat         h          it
                         isfying t e ine q ual y.

v − t1 x − t 2 y − p s ≤ v − t1 x − t 2 (1 − y )− psi − ( p N + k ) w il h av an ince nt e t inst l h e Nav or
                     i
                                                                       l e              iv o     al t      igat

                            e h          e         ore
as a s e cond brow s e r e v n t ough Int rne t Expl r h as al ady been inst l on t e ir com put rs.
                                                             re             aled   h            e
          ion          ure                           al t                              , h
Th e fract of m anufact r i' s consum e rs w h o inst l h e second brow s e r is e q ual t e re fore , to:
       1 pN + k
DN =     −
       2   2t2

               s      s               e     ds h     im pricing pol sum m arized in L m m a 1.
M axim izing it profit from dire ct sal yie l t e opt al          icy                e
 em
L ma1
(i) If t 2 ≥ k t e opt al
                h      im price ch arged by Net  scape is: p N = (t 2 − k )/ 2 .
(ii) If t 2 < k Ne t           l        e o ls                       l o
                    scape w il not be abl t s e l it product dire ct y t consum e rs in cas e of
                     h       ain        ure
disagre e m e nt w it a ce rt m anufact r.


                    o h      e e        y             e                 iat      w
        A ccording t t e abov L m m a onl if th e e xt nt of diffe re nt ion be t e e n brow s e rs is
           l            h                h              alat                               lh
sufficie nt y h igh so t at it e xceeds t e cost of inst l ion of a s e cond brow s e r w il t e re be a dire ct
m ark e t for Ne t      s       .
                  scape ’product Th e outcom e of th e ne got ions bet e e n t e m anufact rs and
                                                             iat      w       h           ure

3
      e h                               w              t
 Not t at in case of disagree m e nt bet e e n Microsof and a giv n m anufact r i , t e l t r l it ent cust e r
                                                                 e           ure     h at e oses s      ire      om
       o s        it                  t h
bas e t it com pet or since M icrosof is t e onl suppl r of ope rat syst s. Th e re is no point t e re fore , for
                                                 y       ie         ing    em                   , h




                                                         8
 h                                       h          it               e                o
t e s oftw are produce rs depe nds upon t e fe asibil y of dire ct sals of softw are t consum e rs. Th e
      e                           e          h
e xist nce of such a m ark e t det rm ine s t e outside options av abl t Ne t
                                                                  ail e o               s     iat
                                                                             scape in it negot ions.
In t e anal t at f l s I dist
    h     ysis h  olow       inguish , t e re fore , bet e e n t e cas e t at t 2 ≥ k and t2 < k .
                                        h               w       h         h

         In addit      h        iat            so      h                  h         e
                 ion, t e ne got ions depe nd al upon t e dem and facing t e com put r
         ure           ion  h
m anufact rs as a funct of t e price s t ey ch arge and t e e xt nt of re s t ions t ey im pos e on
                                        h                h      e            rict   h
h ype of brow s e r t at t e ir cust e rs can s e lct To deriv t ose dem and funct
te t                 h    h         om            e .         e h                          art
                                                                                  ions I st by
           h      h
assum ing t at bot produce rs do not re s t      h                         o       e ed    h
                                           rict t e ch oice of brow s e r t be s e lct by t e ir
    om    t        aling h                                     ed                      e h      il y
cust e rs;h us inst l t e pre fe rred brow s e r as re q ue s t by each of th e m . Giv n t e ut it
specificat of t e consum e rs, t e dem and facing m anufact r i is giv n4 , t e re fore , by:
          ion  h                h                          ure        e      h

                                                                                                                            (1)
                                                        1 p sj − p s
                                                     Di ( ps , p sj )=
                                                                   i
                                                           +
                                                           i
                                                                     ,
                                                        2     2t1
      e
if e v ry individualpurch ases a com put r and t e e nt m ark e t is serv
                                        e       h      ire                               e h
                                                                         ed. If, h ow e v r, t e price s
             h           ure                 l                      e h
ch arged by t e m anufact rs are s ufficie nt y h igh , it is possibl t at som e consum e rs, w h os e
 ide point are l ed sufficie nt y far aw ay from t e l ion of th e m anufact rs, decide t
“ al      s”   ocat            l                  h ocat                    ure          o
    h           h                 eey                       e                                ure
w it draw from t e m ark e t com plt l and not buy a com put r. Th e dem and facing m anufact r i
    h               e
in t at cas e is giv n by:

                                                                                                                            (2)

                                       Di ( p s , p sj )=
                                                                     i
                                                            v t2 ps
                                              i
                                                              −   −    .
                                                            t1 4t1 t1

   e h        e h h           d                      e          h                   h                    eey
Not t at w h il t e t re s h ol consum e r w h o de t rm ine s t e dem and w h e n t e m ark e t is com plt l
   e                        w              h         e                ure         h h          d
cov red is indiffe re nt bet e e n buying t e com put r from m anufact r i or j, t e t re s h ol
                       ess h    l e                    at                        w              h
consum e r in cas e of l t an ful cov rage of th e popul ion is indiffe re nt bet e e n buying t e
       e              ure                       ion        e        ice toge h
com put r of m anufact r i or forgoing consum pt of com put r s e rv s al t e r. H e nce ,


           to                     e     s                 o h                 om                    ure         e h h
M icrosof t conside r a direct sal of it w eb brow s e r t t e rem aining cust e rs of m anufact r i , giv n t at t e
 at e        ost l om                                      h
l t r h as l al cust e rs in cas e of disagre e m e nt w it M icrosoft.
4
           h      at            ee y      e    h h           d                                      w
  W h e n t e popul ion is com plt l cov red t e t re s h ol consum e r x*w h o is indiffe re nt bet e e n buying from i or j
                                                              }                                                   }
sat s t e e q ual y v − p s − t1 x * − Min { 2 y , t 2 (1 − y ) = v − p s − t1 (1 − x *)− Min{t 2 y , t 2 (1 − y ) . Th e
                             i                                             j
   isfie h      it                          t
                         s       l al e h              .         h
dem and facing i consist of al x v ue s ls s t an x* W h e n t e popul ion is not com plt l cov red t e t re s h ol
                                                                          at                ee y      e    h h    d
                                      w                            h              h                 e
consum e r x*w h o is indiffe rent bet e e n buying from i or w it draw ing from t e m ark et is giv n by:
v − p s − t 1 x * − Min
      i
                                 {t 2 y , t 2 (1 −     y )} Th e dem and facing i consists of al x ≤ x * .
                                                           =0.                                 l


                                                                 9
     e     h                  h
w h il in t e form e r cas e t e m anufact rs com pe t against e ach ot e r in at ract cust e rs in
                                          ure         e                h         t ing     om
 h at e                        ure       ocal     y e           ain                      at
t e l t r cas e e ach m anufact r h as a l m onopol ov r a ce rt s e gm e nt of th e popul ion.
In addit        e h h           ying assum pt in t e deriv ion of th e dem and in (1) and (2) is
        ion, not t at t e unde rl            ion  h       at
 h                e           ure      o
t at e ach com put r m anufact r h as t q uot a singl price for it com put rs irre s pe ct e of w h ich
                                             e      e             s       e               iv
                         ed      om                    ure                   e            h
brow s e r is re q ue s t by cust e rs. M ost m anufact rs post indeed a singl price for t e ir
                        iv
m ach ine s irre s pe ct e of th e t                  h       al on .
                                    ype of softw are t ey inst l it
          If m anufact r j doe s not im pos e re s t ions on cust e rs w h il m anufact r i re s t s
                      ure                           rict         om         e          ure        rict
 h               s    om
t e ch oice of it cust e rs t a singl brow s e r (e it e r be caus e it coul t re ach an agre e m e nt w it
                             o      e                 h                    dn’                             h
                                                            ed s
one of th e softw are produce rs or becaus e M icrosoft bundl it brow s e r as part of th e ope rating
    e      h                      l ow        h                        ure         om            h
syst m ), t e dem and facing i w il be l e r t an (1) or (2). M anufact r i' s cust e rs can e it e r
      h       e                                            aled                                            h
us e t e s ingl w eb brow s e r of M icrosoft th at is inst l by i or purch as e a s e cond brow s e r at t e
                 l
price p N dire ct y from Ne t                            e                s.
                             scape , if such a dire ct sal m ark e t e xit Th e consum e r of type (x, y)

              il y e e       [
deriv s t e ut it lv l v − t1 x − Min{t 2 y , (t 2 (1 − y )+ p N + k )} p s
     e h                                                               − i           ]as a re s ul.
                                                                                                  t    If th e s am e

                   o     ch o        ure               il y    d
consum e r w e re t sw it t m anufact r j h e r ne t ut it w oul be
[ − t (1 − x )−
v     1               t                }     ]
                  Min{ 2 y , t2 (1 − y ) − p sj . Giv n t e abov ne t ut it expressions I deriv in L m m a
                                                     e h        e       il y                   e    e

   h                          ure
2 t e dem and facing m anufact r i if it is t e onl one t re s t t e ch oice of cust e rs. Al
                                             h    y      o      rict h              om      l
           e
proofs of L m m as and Proposit            uded in t e A ppe ndix.
                               ions are incl        h


 em
L ma2
                 ure        rict h              s    om     o h       e
W h e n m anufact r i re s t s t e ch oice of it cust e rs t t e s ingl w eb brow s e r offe red by
         th
M icrosof t e n:
        h                    eey     e         h          it                               rict    h
(i) If t e m ark e t is com plt l cov red and t e com pe t or doe s not im pos e any re s t ions, t e
                        5
dem and facing i is:




5
                 e           ibrium w h e re bot m anufact rs are act e in t e m ark et im pl
 I assum e an int rior e q uil                  h         ure        iv     h          ,          h
                                                                                            ying t at e ach face s a
     iv ev of
posit e l el dem and.


                                                            10
                                                                                                         (3)
                                          1 p sj − p s (t2 + k )(3t2 − k )
                                                        i

                                         2 +              −                     if t2 ≥ k
                                                2 t1            32t1t2
                        Di ( ps , p s )= 
                              i      j   
                                         1 p j − p i t
                                          + s        s
                                                          − 2                    if t2 < k
                                         2
                                              2t1           8t1


                                   eey     e     h
(ii) If th e m ark e t is not com plt l cov red t e dem and facing i is :

                                                                                                         (4)
                                           v     t 2 p si (t2 + k )(3t2 − k )
                                           t −       −
                                                  4 t1 t1
                                                          −
                                                                 16t1t2
                                                                                 if t2 ≥ k
                                           1
                        Di ( p s , p sj )= 
                               i           
                                           v           i
                                                  t2 ps t2
                                            −       −    −                      if t2 < k
                                           
                                            t1   4t1 t1 4t1


A com parison of (3) and (4) w it (1) and (2) indicat s t at t e reduct in t e dem and facing i as
                                 h                   e h      h        ion  h
        t                 ion       rict                 ch                  e                       e
a re s ul of th e im posit of re s t ions on consum e rs’ oice is m ore s e v re w h e n a dire ct sal
m ark e t for Ne tscape ’product doe s not e xist (i.e . t2 < k .)
                        s


              h                 rict h                      om     o h      e
        If bot produce rs re s t t e ch oice of th e ir cust e rs t t e singl w eb brow s e r offe red
            th                                                                                 e el
by M icrosof t e dem and facing e ach re m ains as spe cified in (1) if th e m ark e t is com plt y
   e         h  ocal
cov red. W it a l m onopol h ow e v r, e ach produce r l som e cust e rs due t t e
                         y,        e                   oses        om         o h
      rict                                           il as
re s t ions it im poses. Th e dem and facing it is st l spe cified in (4).


        iat      w           er
3. Negot ions Bet een Com put M anufact              w                       h
                                       urers and Soft are Com panies w h en t e
                     et y
    M ark et is Com pl el Covered.
                   o   e igat h                          iat       h        ibria I conside r first as a
        In orde r t inv s t e t e e ffe ct of th e ne got ions on t e e q uil                      ,
             h         h      h                       lh              s      l o
bench m ark t e cas e t at bot softw are produce rs sel t e ir product direct y t consum e rs.
                             h           o     e o     al t                     s h        v        h
Consum e rs are as s um ed, t e re fore t be abl t inst l h e s oftw are product t e m s e le s w it out
             h        ice      e                e
re q uiring t e s e rv s of int rm ediarie s . L t k W be t e cost of inst l t e ope rat syst m and
                                                           h              aling h       ing  e

   h              aling h             h w                         h
k t e cost of inst l e it e r one of t e t o w eb brow s e rs by t e consum e rs. W h e n M icrosoft



                                                           11
              e s                 h s       ing  e          s h                              h
doe s not bundl it brow s e r w it it operat syst m it s e t t e price rW for W indow s and t e

price rE ≡ (rT − rW   ) for th e Expl r.
                                    ore        Ne t           s h                h     igat
                                                   scape s e t t e price rN for t e nav or. In re s pons e ,

                 h         ing  e                      h h              h                 h
consum e rs buy t e ope rat syst m and com bine it w it t e brow s e r t at m inim ize s t e s um of
h ransport ion and dire ct cost of using t e brow s e r
te t      at                              h
            (                                       }
(i.e . Min { rE + k + t 2 y ) (rN + k + t 2 (1 − y )) .) Assum ing t at t e e nt m ark e t is cov red, t e
                             ,                                      h h         ire              e      h

                                      e h
dem and facing e ach brow s e r is giv n t e re fore , as:
                1 ri − r j
         Dj =     +        , where i , j = E , N E ≠ N .
                2   2t 2

        Th e profit of M icrosoft am ount t (rW + D E rE ) and t os e of Ne t
                   s                       o                    h            scape are D N rN . Th e

part s ch oos e t e ir price s (rN and rE for Microsoft and rN for Netscape ) t m axim ize t e ir
    ie           h                                                             o            h

                                                                                3
          iv       s,   ding t e s ol ion t at rE = rN = t 2 and rW = v −
re s pe ct e profit yie l     h     ut     h                                      t 2 − k W − k , w h e re t e
                                                                                                            h
                                                                                2
at e                                 to
l t r price is ch os e n by M icrosof t e xt      h     ire   us
                                            ract t e ent s urpl of th e consum e r w h o is just
                 w       h w
indiffe re nt bet e e n t e t o brow s e rs.
                               e s w            s oge h
        W h e n M icrosoft bundls it t o product t t e r Ne t             h        uded from t e
                                                             scape is e it e r e xcl          h
m ark e t com plt l if t 2 < k , or it can st l e l it brow s e r as a s e cond brow s e r for t e price
               eey                           il s l s                                           h

p N = (t 2 − k )/ 2 . In t e form e r cas e , M icrosoft s e t t e price rT of it com bined syst m at
                          h                                   s h                s              e

rT = v − t 2 − k W − k . Such a price e xt s t e e nt s urpl of th e consum e r w h o is l ed in t e
                                          ract h     ire   us                            ocat     h

dist     ion h    h
    ribut t e fart e s t aw ay from t e Expl r. W h e n Ne t
                                     h     ore              scape can cont      o ls
                                                                          inue t s e l it brow s e r
in spit of t e bundl st e gy of M icrosoft (i.e . w h e n t 2 ≥ k ,) th e s e gm e nt of th e consum e rs
       e    h      ing rat

w h o ch oos e t inst l s e cond brow s e r am ount t (t 2 − k )/ 4t 2 . Th e h igh e s t price rT t at
                o    al a                          s o                                              h

                             s              e        h             ract h     ire   us
M icrosoft can ch arge for it com bined syst m , in t is cas e e xt s t e e nt s urpl of th e
                     ust               w          aling h   igat                                   h
consum e r w h o is j indiffe re nt bet e e n inst l t e Nav or as a s e cond brow s e r or using t e
                                   (3t 2 + k )
Expl r inst ad (i.e . rT = v −
   ore     e                                     − k W − k .) Th e abov cal at
                                                                       e               y h         t
                                                                          cul ions im pl t e re s ul re ported
                                       4
    e
in L m m a 3.


 em
L ma3




                                                          12
                   h    h      ire              e                               lh           e
        Assum ing t at t e e nt m ark e t is cov red and softw are produce rs sel t e ir syst m s
dire ct y t consum e rs, M icrosoft st l pre fe rs t bundl it product t t e r w h e n t 2 > k .
       l o                            rict y        o    e s         s oge h

O t e rw is e , w h e n t 2 ≤k M icrosoft is j indiffe re nt bet e e n bundl or s e l it syst m s
   h                                          ust               w          ing      ling s   e

         e y.
s e parat l
            h            I       h h           e                  iat      w       h
        In t e s e q ue l sh ow t at t e e xist nce of th e ne got ions bet e e n t e s oftw are produce rs
     h           ure             e      e               w       h                   h
and t e m anufact rs w h o s e rv as int rm ediaries bet e e n t e consum e rs and t e s oftw are
                     e      h      e
com panie s m ay re v rs e t e abov re s ul In part ar, w h e n M icrosoft h as a st
                                          t.       icul                                        iat
                                                                                    rong ne got ing
     ion is-à is h      ure      rict y            o    e s         s oget
posit v -v t e m anufact rs it st l pre fe rs not t bundl it product t h e r.
            art               h        iat                    rict
        I st by conside ring t e ne got ions w h e n no re s t ions on ch oice are im posed, and e ach
                            h    h           ure    al h
                                                      s                                    h      .
consum e r can re q ue s t t at t e m anufact r inst l t e w eb brow s e r sh e pre fe rs t e best Th e
                          h        iat      w                              ure    e h
agre e m e nt payoffs in t e ne got ions bet e e n M icrosoft and m anufact r i ov r t e paym e nts
                            e       low
rTi and rW pe r unit are giv n as fol s:
         i



                                       1 p sj − psi    i 1 i 1 i 1 i 
                                  Si =  +
                                       2               p s − rT − rW − rN 
                                                       
                                             2t1            2    2    2 

                                                                                                          (5)
                    1 p sj − p s
                                i
                                     1 i 1 i  1 p s − p sj
                                                       i
                                                                     1 j 1 j 
                M = +
                   2                rT + rW  +  +
                                     2                              rT + rW  i, j = 1, 2; i ≠ j ,
                          2t1            2  2       2 t1         2
                                                                           2 


w h e re S i is t e payoff of m anufact r i and M t e payoff of M icrosoft in cas e of agre e m e nt
                 h                     ure         h                                                .

   e h                  rict                   f             at
Not t at since no re s t ions are im posed, h al of th e popul ion of consum e rs w h o buy a ce rtain
       e               h    h           ure    al
com put r re q ue s t t at t e m anufact r inst l M icrosoft’Int rne t Expl r and t e s e cond h al
                                                 s          s   e         ore      h              f
           s h     igat     h                  h           ure        h                      o h
re q ue s t t e Nav or. In t e form e r cas e t e m anufact r incurs t e cost rTi according t t e

paym e nt t M icrosoft for a com plt syst m and in t e l t r cas e t is cost is e q ual(rW + rN ),
           o                      ee     e          h at e          h                    i    i



                       o h                     s o
w h ich corre s ponds t t e com bined paym e nt t M icrosoft and Ne tscape .
                                        w                              e           ure  oses s
        In cas e of disagre e m e nt bet e e n i and M icrosoft com put r m anufact r i l it e ntire
    om                             h    y
cust e r base since M icrosoft is t e onl suppl r of ope rat syst m s in t e m ark e t Th e payoff
                                              ie            ing  e        h           .
 o                               h     h                           e el    e       e h
t M icrosoft depends upon w h e t e r t e m ark e t re m ains com plt y cov red aft r t e disagre e m e nt
                  h    low
as spe cified by t e fol ing disagre e m e nt payoffs:




                                                     13
            S i* = 0

                                                                                                              (6)
                                                      if the market remains completely
                 1 r j + 1 r j                        covered
                 2 T 2 W
                 
            M* = 
                  v t         p j 1  1            if the disagreeme nt results in
                  − 2 − s  rTj + rWj 
                  t                 2
                  1 4t1 t1 
                                        2            some consumers being unserved



                                            o h
Th e disagre e m e nt payoffs corre s pond t t e outside opt       ail e o h      ie           h
                                                            ions av abl t t e part s in cas e t ey fail
 o
t re ach an agre e m e nt.
                                  ut     h       e          h           s            o
           Th e Nash Bargaining Sol ion t at de t rm ine s t e paym e nt rTi and rW t M icrosoft
                                                                                  i



              h    low
m axim ize s t e fol ing e xpression:
                                                                                                              (7)

                                               Max (S i − S i* ) 1 (M − M * )
                                                               λ            (1− λ )
                                                                                 1
                                                                                  ,
                                                     i
                                              rTi , rW


           at             w                                e         iv          us    h
If th e re l ionsh ip be t e e n i and M icrosoft ge ne rat s a posit e ne t surpl so t at
[S
 (   i                     ]
         + M )− (S i* + M * ) > 0, t e w e igh t λ and (1 − λ ) det rm ine t e s h are s of th is com bined
                                    h           s 1          1     e        h

    us h           o h           ure     o                      iv y.         h          h al
surpl t at accrue t t e m anufact r and t M icrosoft, re s pe ct e l H e nce t e bigger t e v ue
of λ t e l r t e s h are of th is surpl t at accrue s t t e m anufact r. W h e n λ = 0.5 t e t o
    1 h  arge h                       us h             o h           ure          1       h w

    ie         o             l h
                              y         us
part s agre e t sh are e q ual t e s urpl generat in t e ne got ions, im pl
                                                 ed   h        iat              h                 e
                                                                          ying t at e ach re ce iv s
0.5 (S i + M − S i* − M * ) in e xcess of it out
                                            s   side opt                at                            e
                                                        ion. If th e re l ionsh ip doe s not ge ne rat any

     iv          us h      ies   v h          at              eey       h
posit e ne t surpl t e part dissole t e ir re l ionsh ip com plt l and t e payoff to e ach is
   e             s
det rm ined by it outside option.
               im             h            o
           O pt izing (7) w it re s pe ct t rTi and rW , prov
                                                     i
                                                             ided t at t e m ark e t re m ains com plt l
                                                                   h    h                           eey

   e      low
cov red fol ing a disagre e m e nt yie l t e fol ing first orde r condit
                                  ,    ds h    low                      ion:

                                                                                                              (8)




                                                          14
                                                 1 i 1 i       1               1 
                          (1 −   λ ) p si − rTi − rw − rN − λ  rTi + rW − rTj − rWj = 0 .
                                  1
                                            1
                                                               1
                                                                       1 i 1
                                           2     2    2        2    2    2     2 


               e h       h           ric
            Not t at at t e sym m e t e q uil
                                            ibrium w h e re bot m anufact rs ch arge ide nt
                                                               h         ure               icalprice s
(p   i
     S   = p Sj ) and pay ide ntical e s t l ns e t e t ch nol (rTi = rTj , rW = rWj , rN = rNj ) M icrosoft
                                    rat o ice      h e       ogy             i          i



            ract  h      ire   us                       h
e nds up ext ing t e e nt s urpl of e ach produce r so t at

                                                                                                               (9 )
                                                  1 i 1 i           1 i
                                                    rT + rW = p si − rN .
                                                  2     2           2


                         ure         e                h         t ing     om         h
H e nce w h e n m anufact rs com pe t against e ach ot e r in at ract cust e rs and t e m ark e t
               eey     e              iv           h                                               h
re m ains com plt l cov red, irrespect e of w h e t e r M icrosoft re ach e s an agre e m e nt w it one of
 h           ure                   il     s
t e m anufact rs, M icrosoft can ut ize it m onopol posit in ope rat syst m s t e l inat
                                                  y      ion        ing  e     o im     e
t e e nt profit of e ach m anufact r irre s pe ct e of th e v ue of λ . In cont , if a
 h      ire    s                  ure            iv          al      1         rast

                     h                     ure       ts                     e ing h          , h
disagre e m e nt w it one of th e m anufact rs re s ul in som e consum e rs lav t e m ark e t t e
   im   ion         ds:
opt izat of (7) yie l

                                                                                                           (10)
            1 p Sj − p S                                                              
                           (1 − λ ) p S − rTi − rW − rN  − λ  rTi + rW − rTj − rWj 
                         i
                                              1     1 i 1 i       1     1 i 1      1
             +                    1 
                                         i
                                                             1                        
            2     2t1                              2       2                2 
                                             2     2                   2    2
                         v t             p j 1    1 
                  − λ  −  − 2 − S  rTj + rWj  = 0
                      1  1                     2
                         t1 4t1 t1 
                                                     2 


     h           ric    ibrium , t e re fore ,
A t t e sym m e t e q uil         h

                                                                                                           (11)
                                  i 1 i
                                  p S − rN 
            1 i 1 i                    2                       i 1 i
              rW + rT =                                       <  p S − rN ,
            2     2        2λ   v t 2
                              1                pi                 2 
                        1+       1−  −      − S         
                                                        
                         1 − λ   t1 4 t1 t1
                              1                          
                                                            




                                                        15
    ying t at M icrosoft can no l r e xt
im pl     h                     onge    ract t e e nt s urpl of e ach m anufact r. Since a
                                              h      ire   us                  ure
                     h           ure   ict                                 h             h
disagre e m e nt w it a m anufact r infl s som e dam age on M icrosoft in t is cas e in t e form of a
    le               om
sm al r bas e of cust e rs--t e ne got ing posit of th e m anufact rs is im prov
                             h        iat       ion               ure           ed.
                  at                rat h    h                 ior               ure    l
        In O bserv ion 1 I de m onst e t at t e pricing be h av of th e m anufact rs w il be such
 h              e                   ibrium w h e re t e m ark e t w il re m ain com plt l cov red
t at it can ne v r support an e q uil                h               l               eey     e
  low                         w                                          ure
fol ing a disagre e m e nt bet e e n M icrosoft and one of th e m anufact rs.


        at
O b serv ion 1
                               ric    ibrium t at is consist nt w it t e m ark e t being ful cov red
        Th e re is no sym m e t e q uil       h             e       h h                    ly   e
   h    h                                                              h                     ure
bot in t e cas e of agre e m e nt and in cas e of disagre e m e nt w it one of th e m anufact rs.


                           e           ure      h           o          h
        Since e ach com put r m anufact r h as t e freedom t ch oos e t e price it ch arge s from
                w                    iv o         h                     l      h
consum e rs it al ays h as an ince nt e t rais e t is price s ufficie nt y so t at som e dam age is
   ict                               s o                             h h           ure          h
infl ed on M icrosoft in cas e it fail t re ach an agre e m e nt w it t e m anufact r. W h e n t e
                     h           ure                 l             ing o                           h
price s ch arged by t e m anufact rs are s ufficie nt y h igh , fail t re ach an agre e m e nt w it one
              ie h                                                   toge h    h             h
of th e m im pl s t at som e consum e rs drop out of th e m ark e t al t e r, t us reducing t e num ber
       e     h                   e o l    .
of syst m s t at M icrosoft is abl t s e l Not t at M icrosoft's inabil y t e xt
                                              e h                     it o            h
                                                                                ract t e entire
    us                  ure    h                                h          ion h   y ine
surpl of e ach m anufact r in t is cas e doe s not depend upon t e assum pt t at onl l ar
t                                                   h        iat      e      h   ine
 ransfe r price s ( rT and rW ) are conside red in t e ne got ions. Ev n w it nonl ar (transfe r)

              e h             ure       il s e h              h                 h
price s ch eduls t e m anufact rs can st l e lct t e price s t ey ch arge from t e consum e rs to
       e h                oses           e o                             h                   ong
guarant e t at M icrosoft l if it is unabl t re ach an agre e m e nt w it one of th e m . As l as
 h                                 iat      w       h           ure                    eey         ess
t e re is som e product diffe re nt ion be t e e n t e m anufact rs, e ach is not com plt l pow e rl
    h        iat       h
in t e ne got ions w it M icrosoft.
                      ure           s       o             s                               ding t e first
        Each m anufact r ch ooses it price t m axim ize it agre e m e nt payoff S i , yie l     h

orde r condition:

                                                                                                      (12)
                                                 1 i 1 i 1 i
                                                   rT + rW + rN
                                      1 p − 2p
                                            j
                                                 2
                                                   i
                                                       2     2
                                        +   S
                                               +   S
                                                                =0
                                      2   2 t1          2 t1




                                                       16
            h         ion  h         ds h
Com bining t is condit w it (10) yie l t e fol ing sol ion for t e price of a ne w com put r,
                                             low     ut         h                         e
              e                   iat    e
    p S , in t rm s of th e ne got ed rat agreed w it Ne t
                                                     h                     h          ric    ibrium .
                                                          scape , rN , at t e sym m et e q uil

                                                                                                                   (13)

                                                                    t                   1 
                                                                  2
                               t 2 rN            t 2 rN                 (1 + λ )
                              v −  +  +         v −  −   − 4t1 v − 2 −
                                                                   
                                                                                   1
                                                                                     t1 − rN 
                                  4 2               4 2            4     2λ         2  
                       pS =
                                                                                 1

                                                             2

                        o        rat h    h
           It is e asy t dem onst e t at t e abov s ol ion yie l indeed l t an ful cov rage of th e
                                                 e   ut        ds       ess h    l e
                                                                 t2
popul ion in cas e of disagre e m e nt since p S > v − t1 −
    at                                                                    ying t at a m anufact r l ed at
                                                                    , im pl     h              ure ocat
                                                                 4
                                                iv      us o h             ocat     h    h
one e nd of th e m ark e t cannot offe r a posit e s urpl t t e consum e r l ed at t e ot e r e nd of
 h               e h          ibrium price of ne w com put rs.
t e m ark e t giv n t e e q uil                           e


                              h        iat      w
           Ne xt I conside r t e ne got ions bet e e n Ne t           h           ure           iat
                                                           scape and t e m anufact rs. In ne got ing
    h         ure   h    l
w it m anufact r i t e fol ing are t e agre e m e nt payoffs t at accrue t t e part s :
                          ow        h                         h           o h      ie
                                      1 p j − psi
                                                        i 1 i 1 i 1 i 
                                 Si =  + s
                                      2                p s − rT − rW − rN 
                                                       
                                           2 t1              2    2    2 

                                                                                                                   (14)
                                 1 p j − p si      1 i  1 p s − p sj
                                                                 i
                                                                                  1 j 
                              N = + s
                                 2
                                                    rN  +  +
                                                    2  2
                                                                                  rN 
                                                                                  2 
                                      2 t1                      2 t1          
                                w
In cas e of disagre e m e nt bet e e n Net                   ure   h at e       als e           ore
                                          scape and m anufact r i t e l t r inst l Int rne t Expl r
on e ach of it com put rs irre s pe ct e of th e pre fe re nce s of it cust e rs.6 Since t e com pe t
              s       e               iv                              s    om             h          ing
m anufact r t ors t e inst l ion t t e cust e r’t e s t e dem and facing i decl s
         ure ail h        alat    o h      om s ast h                         ine
           o h              ion
according t t e s pe cificat in (3). Ne t          inue o     e h          it s ie s        l
                                         scape cont s t s e rv t e com pe t or’cl nt as w e l
as sel it softw are dire ct y t som e of i' s cust e rs if such a dire ct sal m ark e t e xist (t 2 ≥ k ).
     ls                    l o                    om                        e                 s

                                        , h
Th e disagre e m e nt payoffs are e q ual t e re fore , to:
w h en    (t 2 ≥ k )


6
                        h
 A disagre e m e nt w it Net                     t e h            l e                    at             h         ure
                            scape does not re s ul in ls s t an ful cov rage of th e popul ion since bot m anufact rs
cont      o       e h
    inue t s e rv t e m ark e t.


                                                          17
                                          1 p j − p s (t 2 + k )(3t 2 − k ) i
                                                                            ( p s − rTi )
                                                     i
                                   S i* =  + s
                                          2           −                    
                                               2 t1          32 t1 t 2     

                                                                                                                      (15.a)
                       1 p i − p sj     rNj (t 2 + k )(3t 2 − k )rNj (t 2 − k )2      1 p sj − p s t 2 + k 
                                                                                                    i
                  N* =  + s
                       2                +
                                        2                            +                 +
                                                                                       2             −       
                            2t1                     32t1t 2              8t 2               2 t1      4t1 


w h e n (t 2 < k )

                                                  1 p j − ps t2  i
                                                                    ( p s − rTi )
                                                            i
                                           S i* =  + s
                                                  2          −
                                                       2t1     8t1 
                                                                    

                                                                                                                      (15.b )
                                                 1 p i − p sj      rNj t 2 j
                                            N* =  + s
                                                 2                 +
                                                                    2 8t rN
                                                      2 t1                1


                 h                    ut      h
            A t t e Nash Bargaining Sol ion, t e paym e nt rN t at is negot ed bet e e n m anufact r i
                                                            i
                                                               h           iat    w               ure

and Ne t         v h        low              ion  e
        scape s ole s t e fol ing m axim izat problm :
                                                                                                                        (16)

                                              Max (S i − S i* ) 2 (N − N * )
                                                              λ            1− λ
                                                                                   ,
                                                                               2


                                                i
                                               rN

prov      h    h           us
    ided t at t e ne t surpl generat in t e t
                                    ed            ion w        h            iv         y
                                         h ransact be t e e n t e m is posit e , nam e l if
[S
(    i                    ]
         − S i* )+ (N − N * ) is posit e . If t e l t r is negat e t e part s fail o re ach an agre e m e nt
                                      iv       h at e           iv h       ie     t                         .

Th e param e t r λ in (16) corre s ponds t t e s h are of th e ne t surpl (if posit e ) th at accrue s t
              e 2                         o h                           us         iv                   o

t e m anufact r in t e negot ions w it Ne t
 h           ure    h       iat       h    scape . H e nce a bigge r v ue of λ corre s ponds t an
                                                                      al      2               o

       ed               ion  h
im prov bargaining posit of t e m anufact r. O pt izing w it re s pe ct t rN yie l
                                         ure     im         h            o i     ds:

w h en      (t 2 ≥ k )
                1 p sj − p s
                 +
                            i
                                        (r i − r i ) r i  (t + k )(3t 2 − k ) (1 − λ )( p i − r i )+ λ r j
                                (1 − λ ) T W − N  + 2                               [                          ]
                2                     2                                              2     s    T      2 N
                      2 t1                  2        2        32t1t 2

                                                                                                                        (17)




                                                              18
                                                  (t 2 − k )2 1
                                                              
                                                                        p sj − p s (t 2 + k ) 
                                                                                 i
                                                                                              = 0
                                           + λ               2 +                  −
                                                                                       4 t1 
                                              2
                                                      8t 2                 2t1               


if

                                                                                     ( i
                                  1 p sj − p si  rTi − rW  (t 2 + k )(3t 2 − k ) p s − rTi − rNj )
           (S i − S )+ (N − N )=  2 + 2 t  2  +
                                                           i
                  *                 *
                  i                                         
                                           1                               32 t 2 t1
                                  (t − k )2 1 p sj − p si t 2 + k 
                                             +                      > 0
                                − 2                          −
                                     8t 2  2
                                                   2 t1         4t1 
                                                                     
and w h e n t 2 < k




                                                                                                                       (18)
                      1 p sj − p s             r i − r i    rN 
                                                                2  + λ 8t rN + (1 − λ )8t ( p s − rT )= 0
                                  i                               i
                                        (1 − λ ) T W
                                                                          t2 j           t2 i
                       +
                      2                         
                                                2 
                                                               −       2              2
                                                                                                      i

                            2 t1                2                     1              1




if
                                               1 p sj − p s                 (rTi − rW ) t 2 i
                         (Si − S )+ (N − N )= 2 + 2t                                          ( ps − rTi − rNj )> 0
                                                           i                          i
                                *
                                i             
                                                  *
                                                                            
                                                                             2          +
                                                       1                                 8t1

Not from (17) and (18) th at t e ne got ed paym e nt rN is l e r t e s m al r is t e gap (rTi − rW ),
   e                          h        iat            i
                                                           ow     h       le      h              i



      y h        l h
                  e
nam e l t e s m al r t e price diffe re nt paid t M icrosoft bet e e n a com plt syst m and an
                                          ial    o              w             ee     e
       ing  e    y.       icul                       e    e h
ope rat syst m onl In part ar, w h e n M icrosoft int grat s t e brow s e r as part of th e
ope rat syst m so t at rTi = rW circum st
       ing  e      h          i
                                                                            h           ure    ual
                                         ance s m ay aris e unde r w h ich t e m anufact rs act l y

re fus e t ne got e w it Ne t
          o      iat    h    scape (w h e n (S i − S * + N − N * )< 0 ). W e ch aract rize t os e
                                                                                     e      h

circum st                 at
         ance s in O bserv ion 2.


        at
O b serv ion 2
If M icrosoft int grat s t e brow s e r as part of th e ope rat syst m so t at rTi = rW Ne t
                 e    e h                                      ing  e      h          i
                                                                                            scape m ay

         e o                             h h                            ure                          l
not be abl t re ach an agre e m e nt w it e it e r one of th e m anufact rs w h e n t1 is sufficie nt y

    l.          l
sm al Spe cifical Ne t
                 y,                  osed from t e ne got ions.
                      scape is fore cl          h        iat



                                                                   19
(i)     W h e n t2 ≥ k

                                  (t + k )(3t 2 − k ) (t 2 + k )(3t 2 − k ) 
        if t1 ≤t1* w h e re t1* ∈  2
                                                     ,                      
                                                                             
                                       16t 2                  8t 2          
                                        t2
(ii)    and w h e n t 2 < k , if t1 <      .
                                        2


    l h
In al ot e r circum st                                e h           iat      w       h           ure
                      ance s , M icrosoft cannot pre v nt t e ne got ions bet e e n t e m anufact rs
and Ne t         e                e    e h                                      ing  e
        scape e v n w h e n it int grat s t e brow s e r as part of th e ope rat syst m .
                                   iat      w             e           ure    e          h           iat
        Th e degre e of diffe re nt ion be t e e n com put r m anufact rs det rm ine s t e ir ne got ing
     ion is-a-v M icrosoft and Ne t
posit v        is                                                             iat
                                   scape . H igh e r de gre e s of diffe re nt ion pe rm it e ach
         ure o    ure arge                   us       ed   h        iat              us
m anufact r t capt a l r sh are of th e s urpl generat in t e ne got ions. Th is surpl is
arge
l r, in t      h
         urn, t e h igh e r t e w il
                             h     l         o           om
                                    ingness t pay of cust e rs. Enh anced freedom of ch oice
   w                              h      l
bet e e n brow s e rs incre ases t is w ilingness t pay. As a re s ul w h e n m anufact rs can e xpe ct t
                                                   o                t,                 ure               o
e xt       arge                    us       ed      re                    at e y arge
    ract a l r sh are of th e s urpl generat dow nst am (w h e n t1 is re l iv l l ) th ey h ave

              o                           o h         om       e                        e    e
good re ason t offe r freedom of ch oice t t e ir cust e rs e v n w h e n M icrosoft int grat s
   ore                                at       at h       h      uat                ,        e
Expl r as a part of W indow s. O bserv ion 2 st e s t at t e s it ion is diffe re nt h ow e v r, w h e n
         ure    ain y   e
m anufact rs obt onl a v ry sm al sh are of th e s urpl in t e ne got ions (w h e n t1 is sm al
                                l                     us    h        iat                      l).

In t at cas e , w h e n rTi = rW , m anufact rs m ay re fus e t ne got e w it Ne t
    h                          i
                                            ure                o      iat    h           toge h
                                                                                  scape al t e r.

                 e              h                        e o      e h           iat      w
        D e s pit of th e fact t at M icrosoft m ay be abl t pre v nt t e ne got ions bet e e n
       e           ure
com put r m anufact rs and Ne t               l al                               y e h             l
                               scape (for sm al t1 v ue s ), it is not ne cessaril clar t at it w il

           ant       o              ,    h            I         rat h
find it adv age ous t do so. In fact in t e s e q ue l de m onst e t at M icrosoft m ay earn h igh e r
profit if it s e lct t e gap ∆ ≡ rTi − rW in such a m anne r t at support negot ions w it Ne t
      s          e s h                  i
                                                              h          s     iat       h    scape .

H ow e v r, h igh e r v ue s of ∆ yie l l r v ue s of th e ne got ed rat rN w it Ne t
        e              al             d arge al                  iat    e       h    scape , w h ich

          h        s                         o                           o             s
reduce s t e profit of M icrosoft according t (11). H e nce , in orde r t m axim ize it ow n profits
     e         ing h     iat      w               ure
w h il s upport t e negot ions bet e e n m anufact rs and Ne t                        d
                                                              scape , M icrosoft sh oul ch oos e
t e diffe re nce ∆ t be at t e s m al s t possibl lv l h at st l
 h                  o       h       le          e e e t                 s           iat
                                                              il support such ne got ions. Th is
l e r bound on ∆ is det rm ined by t e re q uire m e nt t at (S i − S * ) + ( N − N * ) = 0. Using t e abov
ow                     e            h                    h            i                             h      e

      at             e                ion                                         usionary
observ ion I ch aract rize in Proposit 1 M icrosoft's profit m axim izing non-e xcl


                                                          20
       ibrium (t at support negot ions bet e e n com put r m anufact rs and Ne t
e q u il        h          s     iat      w             e           ure         scape ) w h e n it
   ualy     h
act l h as t e abil y t e xcl Net
                  it o      ude                ing s         oge h
                                 scape (by bundl it product t t e r).


        ion
Proposit 1
                                  l      l h                           e         iat       h
        W h e n t 1 is sufficie nt y sm al so t at M icrosoft can pre v nt ne got ions w it Ne tscape by

ch oosing ∆ = 0, t e e xist nce of a non-e xcl
                  h        e                                ibrium re q uire s t at ∆ > 0 so t at
                                             usionary e q uil                   h             h
(S i − S * ) + ( N − N * ) ≥ 0. Th e non-e xcl
         i                                                  ibrium t at ge ne rat s t e h igh e s t profit t
                                             usionary e q uil       h            e h                      s o
                 h    low           e ics:
M icrosoft h as t e fol ing ch aract rist


                                  1 t 2 + k 
                                   −
                                   2                
             ( t 2 − k )
                          2
                                           4t 1    
                                                            if t 2 ≥ k
              4t 2             1 ( t 2 + k )(3t 2 − k ) 
        rN =                   −                        
                               2                         
                                        16 t 1 t 2      
             
                                                           if t 2 < k
                                    0


                                                                        r  (1 − λ1 ) 2
                                                                           2
                                  t           r          t
                              v − 2 − 2 t 1 − N +    v − 2 − 2 t 1 − N  +        4t 1
              rT + rW              4           2          4           2   2 λ1
        M=            =
                  2                                         2


           e h    h       iat    e
        Not t at t e negot ed rat rN bet e e n Ne t
                                        w                                   ure   ow     h    h
                                                   scape and e ach m anufact r is l e r t an t e

price Net                                                 o    al a
         scape ch arge s from consum e rs w h o ch oos e t inst l s e cond brow s e r by buying it
       l
dire ct y from Ne t               h            e                     y     e   oyal
                   scape . Since t e dire ct sal price p N is paid onl by v ry l consum e rs w h o

                                                   1 t + k              
    e
h av a strong pre fe re nce for t e Nav or i.e. y > + 2
                                 h     igat                              , w h il t e negot ed price rN is
                                                                                 e h        iat
                                                   2   4t 2             
paid by t e m anufact r on be h al of a l r group of consum e rs ( y > 0.5 ) w h o re q ue s t t is
         h           ure         f      arge                                                    h

brow s e r, Ne t                o          ow                               urn   h arge ol
                scape agre e s t acce pt a l e r paym e nt pe r unit in re t for t e l r v um e of
  e       e so h                  e
sals . Not al t at if a dire ct sal m ark e t doe s not e xist Net                 o
                                                                  scape is forced t acce pt a paym e nt
               s
of ze ro for it brow s e r.




                                                          21
                ion        e        h        ibrium w h e n t e price diffe re nt (rT − rW ) is ch os e n
        Proposit 2 ch aract rize s t e e q uil               h                   ial

 o               l      l h
t be s ufficie nt y sm al so t at ne got ions bet e e n t e m anufact rs and Ne t
                                        iat      w       h           ure         scape are not
fe asibl. Th is ch aract rizat appl s , in part ar t t e cas e t at rT = rW w h ich corre s ponds t
       e                e     ion ie           icul o h         h                                  o

 h     e    ion    e         ore                                 ing  e
t e int grat of Int rne t Expl r as part of th e W indow s operat syst m .


        ion
Proposit 2
W h e n t1 is sufficie nt y sm al and t e price diffe re nt ∆ = (rT − rW ) is so sm al t at m anufact rs
                         l      l      h                   ial                       lh              ure

                 iat       h
bre ak off ne got ions w it Ne t         h                         e o                    e
                                scape , t e price of a ne w com put r t consum e rs is giv n by:



                                                 (1 − λ )
                                            2
                    t2      t2         
               v−      +   v −   − 2t1  + 4t12        1

                    2          2                 2λ
        pS =                                          1

                                   2

     h        s
and t e profit of M icrosoft are :



                                                                       (1 − λ )
                                                               2
                               t                 t2          
                           v − 2 − 2 t1 +       v −    − 2t1  + 4t12        1

                                2                   2                  2λ
        M = p S − t1 =                                                      1
                                                                                .
                                                      2

                                       o
        A com parison of th e payoffs t M icrosoft from Proposit                 ds h      usion
                                                                ions 1 and 2 yie l t e concl
                        ion
sum m arized in Proposit 3.


        ion
Proposit 3
                 h                    eey     e         h                        iat      w
        W h e n t e m ark e t is com plt l cov red and t e degre e of diffe re nt ion be t e e n
         ure           lh                         e         iat       h
m anufact rs is so sm al t at M icrosoft can pre v nt ne got ions w it Ne tscape , M icrosoft pre fe rs
     o ock          iat                              s            ure       e o
not t bl such ne got ions. It e arns h igh e r profit if m anufact rs are abl t re ach an
                  h
agre e m e nt w it Ne t         h    l
                       scape , t us al ing t e m t inst l h e pre fe rred brow s e r as re q ue s t by each
                                      ow    h     o    al t                                        ed
consum e r.
                 h                 ly
        W h e n t e m ark e t is ful cov red and t e degre e of diffe re nt ion be t e e n m anufact rs
                                        e         h                        iat      w               ure
       l              e           ure                              ion is-a-v M icrosoft. As a
is sm al e ach com put r m anufact r h as a w e ak bargaining posit v        is



                                                            22
      t,                 il s           y
re s ul M icrosoft can ut ize it m onopol posit in t e ope rat syst m s m ark e t in orde r t
                                               ion  h         ing  e                         o
e xt        e   arge port of t e consum e r surpl Th is surpl is h igh e r, in t
    ract a v ry l        ion  h                 us.         us                                h
                                                                                urn, w h e n t e
                     o           w                             o                          h        ing o
consum e r is fre e t ch oose bet e e n brow s e rs according t h e r pre fe re nce s w it out h av t incur
 h
t e additional            al
              cost of inst l t e brow s e r h e rs e l (w h e n h av t buy dire ct y from Ne t
                            ing h                    f              ing o         l           scape ).
         e               ie h ,                          o e      e   ore
Th e abov discussion im pl s t at if M icrosoft decides t int grat Expl r as part of its
       ing  e                     e
ope rat syst m w h e n it h as a v ry strong bargaining posit v
                                                             ion is-a-v com put r m anufact rs,
                                                                       is      e           ure
 h      iv ion                             h      usion of Ne t
t e m ot at for such a decision cannot be t e e xcl                        h
                                                               scape from t e m ark e t.
              aim h           h      e
M icrosoft's cl , t at it is t e conv nie nce of consum e rs it h as in m ind, sounds m ore convincing
    h             ie            ion
in t is cas e in v w of Proposit 3.
                   o       at                          im    e h        abil y           iat
       A ccording t O bserv ion 2, M icrosoft cannot e l inat t e profit it of th e negot ions
    h
w it Ne t               h                        iat     w               ure       at e y
         scape w h e n t e degre e of diffe re nt ion bet e e n m anufact rs is re l iv l h igh . If
                      o    ude
M icrosoft w ish e s t e xcl Netscape from t e m ark e t int grat it brow s e r int t e ope rat
                                            h           , e      ing s             o h         ing
    e                       h                       e o
syst m is insufficie nt in t is cas e . It m ay h av t conside r addit     m                    uding
                                                                      ional e asures such as incl
    usiv y auses in it cont s w it m anufact rs or inst l a bug in t e ope rat syst m
e xcl it cl           s    ract   h         ure        aling        h         ing  e
 h   e     o         ibil y
t at lads t incom pat it w it Ne t
                             h                    .    h           ,            rat h
                                  scape 's product In t e s e q ue l I de m onst e t at such
    usionary pract s are not ne cessaril profit e t M icrosoft.
e xcl             ice                  y       abl o


        ion
Proposit 4
                h                    eey     e         h                        iat      w
       W h e n t e m ark e t is com plt l cov red and t e degre e of diffe re nt ion be t e e n
         ure       at e y                                im t     e    e h                o h
m anufact rs is re l iv l h igh , M icrosoft finds it opt al o int grat t e brow s e r int t e
ope rat syst m so t at rT = rW . If no e xpl e xcl
       ing  e      h                       icit                ice      il              ure
                                                 usionary pract s are ut ized, m anufact rs

           im t        iat    h
find it opt al o ne got e w it Ne tscape , yiel
                                              ding t e fol ing approv rat in t e ne got ions.
                                                    h    low         ed e     h        iat


              (t 2 + k )(3t 2 − k )(1 − λ ) λ (t 2 − k ) 2 1 t 2 + k 
             
                                           2
                                             + 2             −
                                                            2         
                           8t 2                     2t 2        4 t1 
                                                                        when t ≥ k
                              (1 + λ )(t 2 + k )(3t 2 − k ) 
                                                                                2

                             −
                                         2
             
                               1                              
        rN =                               16t1t 2          
             
             
             
              2t1t 2 (1 − λ ) 2                                         when t 2 < k
             [t1 − t 2 (1 + λ2 )]
             4


                                                     23
             ion     icit    rict      h           ure            abl o
Th e im posit of e xpl re s t ions on t e m anufact rs is unprofit e t M icrosoft provided
            t2
t at rN <
 h                        e        it
               . Th e abov ine q ual y is m ore l e l t h ol t e w e ak e r t e ne got ing posit of
                                                ik y o     d h               h        iat       ion
            2
Ne tscape , nam e l w h e n t 2 is re l iv l sm al and λ is re l iv l l .
                  y,                  at e y     l      2      at e y arge

                    o        ion                e             t      e              h                  l
        A ccording t Proposit 4, it is im possibl in ge ne ral o de t rm ine w h e t e r M icrosoft w il
    e       iv o      ude   icit
h av ince nt e s t incl e xpl re s t ions in t e cont s w it m anufact rs. H ow e v r, if
                                    rict      h      ract   h         ure          e
Ne tscape h as a w e ak bargaining posit                rict             ey         abl
                                        ion, such re s t ions are definit l unprofit e . For
                                                                                 t 2 (1 + λ )
instance , w h e n t 2 < k e xcl it cl
                               usiv y auses are unprofit e prov
                                                        abl    ided t at
                                                                     h                      2
                                                                                              < t1 .
                                                                                      4λ  2


                ion               h      icit      ion h  h        iat    e
        Proposit 4 is based upon t e im pl assum pt t at t e ne got ed rat s e cured by
Ne tscape pe rm it it t cov r it fixed cost of product (i.e. 0.5 ⋅rN > fixed cost If th e
                  s    o   e s             s          ion                        .)

      iat    e       e       l,        e
ne got ed rat rN is v ry sm al h ow e v r, Ne tscape m ay be forced out of th e m ark e t w h e n

rT = rW . M icrosoft h as t com pare in t is cas e it profit w h e n Ne t
                           o             h           s      s                         uded w it it
                                                                         scape is e xcl        h s

      s,        h          w                               l            h
profit w h e n t e gap be t e e n rT and r W is sufficie nt y h igh so t at Ne t              iv
                                                                                scape can surv e (i.e .,

∆ ≡ (rT − rW ) h as t be ch os e n so t at 0.5 ⋅r N = fixed cost .) Th e e xcl
                     o                 h                                     usion of Ne tscape need not

         abl    h                l.
be profit e in t is cas e as w e l As point out e arl r, in t e ne got ions w it t e com put r
                                           ed       ie       h        iat       h h         e
         ure
m anufact rs M icrosoft can e xt                                            ed          tipl
                                ract som e of th e efficie ncy gains generat w h e n m ul e brands
                 h                       .           e
are offe red in t e brow s e rs m ark e t It is not clar, t e re fore t at t e e xcl
                                                           h           h    h      usion of Ne tscape is
   ant          e                           o   e                     ion                    o h
adv age ous, e v n w h e n M icrosoft h as t giv up a significant port of th is added gains t t e
       e           ure              h                   ion
com put r m anufact rs, w h ich is t e cas e in proposit 4.


        iat      w           er
4. Negot ions Bet een Com put M anufact              w                       h
                                       urers and Soft are Com panies w h en t e
                ess h    ly
    M ark et is l t an Ful Covered
                                       h        iat      w                            e           ure
        Th e agre e m e nt payoffs in t e ne got ions bet e e n M icrosoft and com put r m anufact r i
       e                low
are giv n from (2) as fol s:
                                   v t2    p s  i 1 i 1 i 1 i 
                                              i
                                   −
                             Si =        −      p s − rT − rW − rN 
                                   t1 4t1 t1        2    2    2 

                                                                                                           (19 )



                                                     24
                    v t     pi         1 i 1 i           v t2     pj    1 j 1 j 
                 M = − 2 − s
                    t
                                         rT + rW
                                        2          +      −
                                                            t       − s     rT + rW 
                                                                             2
                     1 4 t1 t1               2            1 4 t1   t1         2 


                              h
In cas e of disagre e m e nt t e out        ion          ie
                                    side opt of th e part s are obt                    low
                                                                   ained from (4) as fol s:
                                                 S i* = 0
                                                                                                       (20)
                                      v t2  p sj 1 j 1 j 
                                     t 4t − t 2 rT + 2 rW .
                                  M = −
                                    *
                                                  
                                     1    1  1            

       e           ure  oses s   ire             o h         y      ion
Com put r m anufact r i l it e nt m ark e t due t t e m onopol posit of M icrosoft in
       ing  e                       inue o rade w it m anufact r j onl
ope rat syst m s and M icrosoft cont s t t          h         ure    y.
       O bt        h                    ut      h     ut     o         ds:
           aining t e Nash Bargaining Sol ion (t e s ol ion t (7)) yie l

                                                                                                       (21)
                                     rTi + rW
                                            i
                                                         i 1 i
                                              = (1 − λ ) p S − rN 
                                                      1 
                                         2                   2 

            ar o h        t ained in t e pre v
       Sim il t t e re s ul obt       h       ious sect        ure o
                                                       ion, fail t re ach an agre e m e nt w ith
                     ure    ict                           h             le      om
one of th e m anufact rs infl s dam age on M icrosoft in t e form a sm al r cust e r bas e .
                  e h               o
M icrosoft is unabl, t e re fore , t e xt      h
                                         ract t e com plt s urpl generat in t e negot ions w it
                                                       ee      us       ed   h       iat       h
         ure         ,         h               ess h
m anufact rs. In fact w h e n t e m ark e t is l t an ful cov red, each m anufact r h as a l
                                                        ly   e                   ure       ocal
       y     h           , h     re h
m onopol in t e m ark e t t us st ngt e ning it negot ing posit e v n beyond t at obt
                                               s     iat       ion e          h      ained w ith
  l e            h      at
ful cov rage of t e popul ion.
                     ure           h                         e              o            h
       Th e m anufact rs ch oos e t e price s of ne w com put rs in orde r t m axim ize t e ir
                           im             h            o i             h     ut                ds h
agre e m e nt payoffs. O pt izing S i w it re s pe ct t p S and using t e s ol ion in (21) yie l t e

      ts       ed   h    low    e
re s ul re port in t e fol ing L m m a.




                                                   25
 em
L ma3
     h           ric    ibrium w h e re p S = p Sj and rki = rk j ;k = T , W , N , t e fol ing e xpressions
A t t e sym m e t e q uil                 i
                                                                                    h    low

              o h        iat            h             h                                   h        s
corre s pond t t e ne got ed prices w it M icrosoft, t e price s paid by consum e rs and t e profit of
M icrosoft as a funct of th e negot ed rat rN w it Ne t
                     ion           iat    e       h    scape .7

                                          rT + rW 2 (1 − λ ) v t 2 rN 
                                                 =        1
                                                             −    −   
                                             2     (1 + λ )  2 8 4 
                                                         1



                                                 v t  2        rN λ
                                            pS =  − 2 
                                             i
                                                               +     1

                                                  2 8 1 + λ 2 (1 + λ )
                                                             1         1



                                         2 λ (1 − λ ) t 2 rN 
                                                                               2

                                           M=1      1
                                                       v −     −    
                                         t1 (1 + λ )              2 
                                                     2
                                                  1
                                                              4
              e h        ar o h       at          h
           Not t at sim il t t e deriv ions in t e pre v    ious sect               s      s            h
                                                                     ion, M icrosoft’profit incre as e t e
ow        h     e         iat
l e r is t e rat rN ne got ed bet e e n e ach m anufact r and Ne t
                                 w                     ure        scape .                                     e h
                                                                                                      To deriv t is

      iat    e           h                                                 h        iat      w
ne got ed rat I specify t e agre e m e nt and disagre e m e nt payoffs in t e ne got ions bet e e n
         ure
m anufact r i and Ne t           low
                      scape as fol s:
                                        v t     p i  i 1     1 i 1 i
                                  S i =  − 2 − S  p S − rTi − rW − rN 
                                        t
                                         1 4 t1 t1 
                                                         2     2    2 

                                     v t     p i 1 i  v t    p j 1
                                 N =  − 2 − S  rN +  − 2 − S  rNj
                                     t
                                      1 4 t1 t1  2
                                                  
                                                       t
                                                        1 4 t1 t1  2
                                                                    


                        v t 2      p S (t 2 + k )(3t 2 − k ) i
                                                              ( p S − rT )
                                       i

                        −        −     −                                                        t2 ≥ k
                                                                         i

                       t1 4t1
                       
                                     t1         16t1 t 2      
                  Si = 
                   *

                        v                t  i
                         − 2 − S − 2 ( p S − rT )
                              t      pi                   i
                                                                                                  t2 < k
                       
                         t 1 4 t1   t1    4t1 




7
              e h h                    e h         ly   e
    To guarant e t at t e m ark e t is ls s t an ful cov red t e ph ysical e s of each m anufact r sh oul be sm al r t an
                                                              h           sal                   ure     d         e
                                                                                                                 l h
                                                                   v t2    r  λ
2. Im posing t is rest ion at t e sym m e t e q uil
              h       rict     h           ric              ds
                                                  ibrium yiel        −   − N  1 < 0.5.
                                                                   t1 4t1 2t1 1 + λ1




                                                            26
                (t 2 − k )2       v t2     p S 3(t 2 + k )  v
                                               i
                                                                    t   p j 1
                                  −
                                  t       −     −           +  − 2 − S  rNj         t2 ≥ k
                8t 2              1 4 t1   t1      8t1  t1 4t1
                                                                       t1  2
               
            N =
             *

                v t 2               p Sj  1 j
                −               −         rN                                         t 2 < k.
               t1 4 t1
                                     t1  2



                                        h
       In cas e of disagre e m e nt w it i, Ne t          inue o     e s     om         o    l
                                                scape cont s t s e rv j’ cust e rs and t s e l
dire ct y t som e of i’ cust e rs as w e l if a dire ct sal m ark e t e xist (t 2 ≥ k . ) Th e first t rm of
       l o            s     om           l,               e                 s                         e

                   o
N * corre s ponds t Ne t      s                             e      v         h
                        scape ’proceeds from such dire ct sals . Soling for t e Nash Bargaining
  ut     h      isfie
Sol ion t at sat s (16) yie l t e re s ul re port in Proposit 5.
                            ds h        ts       ed          ion


        ion
Proposit 5
                h               ess h    ly   e                           e h           iat
       W h e n t e m ark e t is l t an ful cov red M icrosoft cannot pre v nt t e ne got ions
bet e e n t e m anufact rs and Ne t
   w       h           ure         scape irre s pe ct e of th e diffe re nce (rT − rW ) it s e lct Ev n
                                                     iv                                        e s.  e

w h e n Int rne t Expl r is int grat int it operat syst m so t at rT = rW , e ach m anufact r
           e         ore       e    ed o s        ing  e      h                            ure

            ant       o      iat    h
finds it adv age ous t ne got e w it Ne tscape s ince t e ne t surpl generat in t e ne got ions
                                                       h           us       ed   h        iat
is st l posit e (i.e
     rict y  iv          [S
                         (    i                     ]
                                  − S i* )+ (N − N * ) > 0.)

                  t        ed          ion
       Th e re s ul re port in Proposit 5 is sim il t t e one obt
                                                  ar o h                   h
                                                                 ained in t e previous section
         h                        iat      w       h           ure       at e y               h
w h e n t e degre e of diffe re nt ion be t e e n t e m anufact rs is re l iv l h igh . In bot cases,
         ure     e     at e y rong bargaining posit in t e ne got ions w it M icrosoft,
m anufact rs h av a re l iv l st                   ion  h        iat       h
    ying t at t ey cont
im pl     h    h       inue t t
                             o rade w it Ne t
                                        h             e                        e    e s
                                             scape e v n w h e n M icrosoft int grat s it brow s e r as
                    ing  e           h
part of th e ope rat syst m . As in t e pre vious sect                       l,                    e
                                                      ion, and h e re as w e l M icrosoft can pre v nt
 h        iat       h
t e ne got ions w it Ne t        y
                         scape onl by incl
                                         uding e xpl e xcl it cl
                                                   icit  usiv y auses in it cont s w it
                                                                           s    ract   h
 h           ure          usion of such cl
t e m anufact rs. Th e incl                                     y       abl          e
                                         auses is not ne cessaril profit e , h ow e v r, as is
       ed          ion
re port in Proposit 6.


        ion
Proposit 6
         h               ess h    l
W h e n t e m ark e t is l t an ful cov red, M icrosoft finds it opt al o int grat it brow s e r as
                                   y   e                            im t     e    e s
                                 abl        o   ude   usiv y auses in t e cont s w it
part of W indow s. It is unprofit e for it t incl e xcl it cl          h      ract   h



                                                           27
         ure
m anufact rs prov      h    h
                 ided t at t e ne got ed price rN w it Ne t
                                     iat              h                at e y     l
                                                           scape is re l iv l sm al.

          ly,
Spe cifical w h e n


                     rN
                        < R(t 2 , k )
                      2
w h e re
                                   (t 2 + k )(3t 2 − k )
                                                         if t 2 ≥ k
                                           16t 2
                                  
                    R(t 2 , k ) ≡ 
                                  t                      if t 2 < k
                                  2
                                  4


              o       e
O nce again, t guarant e non-e xcl
                                 usion, t e bargaining posit of Ne t
                                         h                  ion                 d               l
                                                                    scape s h oul be sufficie nt y
              e
             l al                  arge v ue s of λ are ne cessary t support t e ine q ual y incl
w e ak . Sm al r v ue s of t 2 and l     al        2                o         h          it     uded

in Proposit 6.8
           ion
                         iat    e              ion          lh
           If th e ne got ed rat rN of Proposit 6 is so sm al t at Ne t             e o    e s
                                                                       scape is unabl t cov r it

          s,                                      usion w it t e possibil y of ge ne rat a posit e
fixed cost M icrosoft com pare s , once again e xcl         h h         it              ing     iv
        w                 o       e h
gap be t e e n rT and rW t guarant e t at Ne t              iv                             s
                                              scape can surv e . Again, M icrosoft's profit need

                     h    usion.
not be h igh e r w it e xcl


       uding R e m ark s
5. Concl
                 e   e oped a m ode l o e v uat t e lv rage t e ory of product bundl in t e cont xt
           I h av dev l              t     al e h e e        h                     ing   h      e
         iat      w               ist      e                       ls          s o
of ne got ions bet e e n a m onopol and int rm ediarie s w h o s e l it product t consum e rs. I
   e igat         h     h
inv s t ed w h e t e r t e m onopol finds it fe asibl and adv age ous t ut ize product bundl
                                  ist               e        ant       o il                ing
           o ock     iat      w       h     e                      al                  e
in orde r t bl ne got ions bet e e n t e int rm ediarie s and a riv firm w h o com pe t s against
 h         ist         e      ary
t e m onopol in a com plm e nt m ark e t M y re s ul support t e Ch icago Sch ool
                                        .          ts         h                      e ional
                                                                                 conv nt
         h               ing            iv        e             y             e      h
w isdom t at product bundl is ine ffe ct e in e xt nding m onopol pow e r, e v n in t is m odified


                                                                             4λv
8
    W h e n t 2 < k nonexcl
                          usion is profit e , for inst
                                         abl          ance, if t2 <             2
                                                                                        .
                                                                       1 − λ          
                                                                       
                                                                             2
                                                                               + 1+ λ
                                                                           λ
                                                                                     2
                                                                        1             


                                                               28
e nv                              s h                  ion             ist        iat
    ironm e nt w h e re it affe ct t e bargaining posit of th e m onopol in ne got ions w ith
pow e rful             ne
          business part rs. Spe cifical t e m onopol finds fore cl
                                      l h
                                       y,          ist                            it
                                                                 osure of com pe t ors via
    ing h              abl              e
bundl e it e r unprofit e or not fe asibl.
          e h             e il        e        e                              iat
        Ev n t ough I h av ut ized a v ry sim pl approach w h e re diffe re nt ion am ong products
is capt          ocat   l
       ured by a l ional ine ar m ode land w h e re t e out e of th e ne got ions is predict by
                                                     h     com              iat             ed
       h                    ut         ie e h h           ts          e      o
using t e Nash Bargaining Sol ion, I bel v t at t e re s ul can be ext nded t a m ore ge ne ral
specificat                   uit   h    low                                              ion
          ion. Th e basic int ion t at al ing consum e rs freedom of ch oice in consum pt can
            h     h         ist
benefit e it e r t e m onopol or t e int rm ediarie s w it w h om it bargains is l e l t carry ov r t
                                  h     e                 h                      ik y o          e o
           w                       e     e
any m ode l h e re consum e rs h av h e t roge ne ous prefe re nce s am ong products.
             lust iv                  at h            in h     e                  ing  e
        For il rat e purposes I form ul ed t e m ode l t e cont xt of th e ope rat syst m s and
                     s.          ts          ysis
brow s e rs m ark e t Th e re s ul of m y anal appl h ow e v r m ore ge ne ral t any indust
                                                  y,        e                 y
                                                                             l o           ry
            ue            iat       h             ne           h      iv ing            ing.
w h e re infl ncing ne got ions w it business part rs m ay be t e m ot at force for bundl
     e il        h         e        ry
W h il ut izing t e com put r indust e xam pl is useful e xposit
                                            e          for      ional                e ion
                                                                     purposes m y int nt in
 h                                   o                  e udge m e nt on t e D e part e nt of J ice 's cas e
t e pre s e nt pape r h as not been t re nde r a definit j                h          m         ust
                            at     ure            is    y                o    ure h
against M icrosoft. Th e s t ic nat of m y m ode l sim pl insufficie nt t capt t e dynam ics
   oled   h              e              h
inv v in t is cas e as st m m ing from t e e xist nce of ne t ork e xt rnal ie s or t e pot nt t re at
                                                 e           w        e   it         h     e ial h
 o                  ion  h        ing  e
t M icrosoft's posit in t e operat syst m s m ark e t.




                                                     29
                                             R e ferences


            .      l .L Com
                    e
Adam s, W .J and Yel n, J ., “ m odit Bundl and t e Burde n of M onopol Quart rl
                                     y    ing    h                    y,”    e y
       Journalof Econom ics, 19 76, 9 0, 475-9 8.


              l
A gh ion, Ph il           t
               ippe and Bol Pat , "Cont s as a Barrie r t Ent
                           on, rick    ract              o   ry," Am e rican Econom ic
            ie
       R e v w , 19 87, 77, 388-401.


          id,       St   e                                      il                     ure
Bank , Dav "Pane ful ruggl: H ow M icrosoft R ank s W aged a Civ W ar on W indow s' Fut ,"
        l re
Th e W al St e t JournalEurope , 02/01/19 9 9 .


                             it
Bork , R obe rt H ., Th e Ant rust Paradox, Ne w York : Basic Book s, 19 78.


Bow m an, W .S., “                     s     h
                  Tying A rrange m e nt and t e L v rage Problm ,” Yal L R e v w , Nov m ber
                                                 e e         e       e aw     ie      e
       19 57, 67, 19 -36.


                          aim av       ed    h aw        l
Bridis, Ted, "M icrosoft Cl s J a R iddl w it Fl s," Port and O re gonian, 12/04/9 8.


                   Eq ibrium Product Bundl
Ch e n, Yongm in, “ uil                  ing,” Journalof Busine s s , 19 9 7, 70, 85-103.


                     rat                  e ial      it       l        y         ?
Ch e n, Yongm in, "St e gic Bidding by Pot nt Com pet ors: W il M onopol Pe rsist " W ork ing
                   e y        orado at Boul 19 9 8.
       Pape r, Univ rsit of Col           der,


        or,          e i,         L
D ire ct A aron and L v Edw ard, “ aw and t e Fut : Trade Regul ion,”Nort w e st rn
                                           h     ure          at         h      e
            e y aw       ie
       U niv rsit L R e v w , 19 56, 51, 281-9 6.


     , iv             e e        e ical e grat and M ark e t Fore cl
H art O l e r and Tirol, J an, "V rt   Int    ion                  osure," Brook ings Pape rs
                       iv y:
       on Econom ic Act it M icroe conom ics , 19 9 0, 205-276.




                                                  30
                       on,    l oh
                               an,
M cA fe e , R . Pre s t M cM il J n and W h inst M ich ae l ., “ ul
                                                on,        D    M t                y,
                                                                   iproduct M onopol
                 y    ing,        at         ue         e y ournalof Econom ics , M ay
       Com m odit Bundl and Corre l ion of Val s , Quart rl J
       19 89 , 104, 371-84.


                        it     aw                        iv                 e y
Posner, Rich ard A., Ant rust L : An Econom ic Pe rspe ct e , Ch icago: Univ rsit of Ch icago
       Press, 19 76.


                                               ey, oh            usion," Am e rican Econom ic
R asm us e n, Eric, R am seyer, M ark , and W il J n, "Nak ed Excl
            ie
       R e v w , 19 9 1, 81, 1137-1145.


  inge           A., A        A ysis      ing,”J
Sal r, M ich ae l “ Graph ical nal of Bundl     ournalof Busine s s , 19 9 5, 68, 85-9 9 .


       ae                     Com    y
Sch m al ns e e , R ich ard, “ m odit Bundl by Singl-Product M onopol s ,”J
                                          ing      e                ie     ournalof Law
                             19
       and Econom ics , April 82, 25, 67-71.


        on,        D
W h inst M ich ae l ., “             osure, and Excl
                        Tying, Fore cl                                               ie
                                                   usion,” Am e rican Econom ic R e v w ,
            e
       Se pt m ber 19 9 0, 80, 837-859 .


   k     oh                       h                    av            ed           o s
W ile , J n R . and Pe rine , Keit , "M icrosoft Says J a D isappoint Users D ue t It O w n
Sh ort                e             l re
      com ings, M isst ps," Th e W al St e t J     ,
                                              ournal 12/04/9 8.




                                                 31
Appendix


          em
Proof of L m a 2
(i)                               eey     e
        If th e m ark e t is com plt l cov red and t e re e xist a dire ct sal m ark e t for Ne t
                                                    h           s            e                         s
                                                                                                 scape ’
         h               h                     ure
product t e consum e rs t at ch oos e m anufact r i satisfy t e fol ing ine q ual ie s :
                                                             h    low           it


                    1 p j − pSi
                                                                                    1
                  x≤ + S                                            when   0 ≤y ≤
                    2    2 t1                                                       2


                    1 p Sj − p S t 2 (1 − y )− t 2 y
                               i
                                                                              1 p + k
                  x≤ +           +                              when
                                                                        1
                                                                          < y≤ + N          (A.1)
                    2     2 t1           2 t1                           2     2  2t 2


                    1 p Sj − p S ( p N + k )
                               i
                                                                        1 pN + k
                  x≤ +           −                               when     +      < y < 1.
                    2     2 t1       2t1                                2   2t 2


   e h        e h                   h h                  e            al a
Not t at w h il t e consum e rs in t e t ird re gion abov buy and inst l s e cond brow s e r,
                h                           e         ore
consum e rs in t e s e cond re gion us e Int rne t Expl r e v n t ough t ey w oul h av pre fe rred t
                                                             e h        h       d     e             o
      h     igat
us e t e Nav or.
           e    ing e h       e h                         h                   ed
        Int grat ov r t e abov t re e re gions and using t e expressions deriv for p N

    e            ds h                                      at                                   e
In L m m a 1 yie l t e dem and specified in (3). Th e deriv ion of th e cas e w h e n dire ct sals of th e
   igat               e     e        ar.      y                  h    h h
Nav or are not fe asibl is v ry sim il Th e onl diffe re nce is t at t e t ird re gion of (A.1)
                     h
doe s not e xist in t is cas e .
                 ure         ocal     y e                              at              ide point
(ii) If m anufact r i h as a l m onopol ov r a s e gm e nt of th e popul ion w h os e “ al      s”
    ocat  os o , s        om
are l ed cl e t it it cust e rs satisfy t e fol ing ine q ual ie s prov
                                         h    low           it               h h
                                                                       ided t at t e re is a dire ct
  e
sal m ark e t for Ne t      s
                      scape ’brow s e r.
                       v − p s − t2 y
                             i
                                                                      1 p + k
                  x≤                                      if    0 ≤y ≤ + N
                            t1                                        2  2t 2

                                                                                                      (A.2)
                       v − p S − t 2 (1 − y )− ( p N + k )
                             i
                                                                1 pN + k
                  x≤                                       if     +      < y ≤1.
                                        t1                      2   2t 2


                                                           32
                 at
Proof of O b serv ion 1
                  ure          h             s       e o               s                         ding
    Each m anufact r ch ooses t e price of it com put r t m axim ize it agre e m e nt payoff yie l
for i:
                                 1 i 1 i 1 i
                                   rT + rW + rN
                 ∂ i 1 p − 2p
                  S           j
                                 2     2
                                         i
                                             2 .
                      = +     S
                               +         S

                 ∂S 2
                  p i
                          2 t1          2 t1


              ric    ibrium w it ful cov rage post
If a sym m e t e q uil          h  l e                                    ed, h    e
                                                  -disagre e m e nt e xist t e abov e xpression
    d w              iv    e h         us    ract       ion at
w oul al ays be posit e giv n t e s urpl e xt ion condit st ed in (9 ). H e nce, each
              d     e          iv o          s       o h                    e e e t               e
produce r w oul h av an ince nt e t rais e it price t t e h igh e s t possibl lv l h at is consist nt
    h  l e                         .                d
w it ful cov rage of th e m ark e t Th is price w oul be set so t at t e s urpl of th e t re s h ol
                                                                 h    h       us         h        d
consum e r of type x = 0.5 is com plt l ext ed, nam e l p S = v - 0.5t1 - 0.25t 2 . H ow e v r, if
                                   eey     ract       y,                                    e

m anufact r i raises t e price e v n furt e r t p S = v − 0.5t1 − 0.25t 2 + ε w it ε > 0, t e m ark e t
         ure          h           e      h     o i                                h        h

w il be l t an ful cov red and t e m anufact r's sh are w il decl t (0.5 − ε / t1 ). For fixed
   l ess h       ly   e         h           ure            l ine o

                       e             h
re im burs e m e nt rat s agreed w it M icrosoft and Ne t                 o
                                                         scape according t (9 ) (i.e .,
1 i 1 i 1 i
  rT + rW + rN = v − 0.5t1 − 0.25t 2 ) such a dev ion w il benefit i since it raises it profit from
                                                 iat     l                             s      s
2     2    2
ze ro t (0.5 − ε / t1 )ε. H e nce , a cont
       o                                        ion o h        ion   l e
                                          radict t t e assum pt of ful cov rage .                            Q.E.D .


     at
Deriv ion of Disagreem ent Payoffs of Netscape: Equations (15.a) and (15.b )
         W h e n t 2 ≥ k Ne t            e h        om                    ype         h
                             scape s e rv s t e cust e r of j w h os e y t is bigger t an 0.5. Th e m ass

               om
of th os e cust e rs is obt                     h    low      e
                           ained from (A.1) by t e fol ing int gration:


                             1 pN + k
                              +
                             2 2 t2                  1                         1               1

                                  ∫                  ∫ dx dy +                 ∫               ∫dx dy
                                  1     1 p Sj − pS t2 (1− y )− t2 y
                                                  i                         1 pN + k
                                                                             +         1 p Sj − pS p N + k
                                                                                                 i
                                          +         +                                    +         −
                                  2     2    2 t1         2 t1              2 2 t2     2    2 t1     2 t1


                                                 1 p + k 
In addit cust e rs of i of y t
        ion  om               ype in t e re gion  + N
                                      h                           al a
                                                          ,1 inst l s e cond brow s e r by
                                                 2  2t 2   
              l
buying dire ct y from Ne tscape . Th e ir m ass is obt                      low
                                                      ained from (A.1) as fol :


                                                                       33
                                                   1 p S − pS p N + k
                                                       j     i
                                                     +         −
                                           1       2    2 t1     2 t1

                                           ∫
                                        1 pN + k
                                                           ∫
                                                           0
                                                                        dx dy
                                         +
                                        2 2 t2




     it ing            e            ds h                                      e h          w
Subst ut for p N from L m m a 1 yie l t e e xpression for N * in (15.a). W h il t e first t o

 e                   o    e
t rm s corre s pond t re v nue s obtained from m anufact r j t e l t rm corre s ponds t re v nue s
                                                        ure   h ast e                  o    e
obt                     e o     om                   al a                    h        v
   ained from dire ct sal t cust e rs of i w h o inst l s e cond brow s e r t e m s e le s .
        W h e n t 2 < k t e deriv ion for N * is sim plr since t e re v nue s t at accrue t Ne t
                         h       at                   e         h      e       h           o    scape
     l ained from t e agre e m e nt w it m anufact r j.
are al obt         h                    h         ure                                                Q.E.D .


                 at
Proof of O b serv ion 2
Subst ut int (17) and (18), sym m e t as w e l as rT = rW yie l
     it ing o                        ry      l                ds:

                                                                                                           (A.3)


                                                            rN 
                                  (t 2 + k )(3t 2 − k )t1 − 2  (t − k )2      1 (t 2 + k ) 
                                                               − 2            −             when t 2 ≥ k
                                                                               2      4 t1 
                                               32t1t 2                8t 2                    
                                  
   D ≡ (S i − S i ) + ( N − N ) = 
                *            *

                                  
                                  
                                   t2       rN                                                when t 2 < k
                                  8t t1 − 2 
                                   1             


        ut                  ied
Th e s ol ion for rN as im pl by (17) and (18) is




                                                         34
                                                                                                                  (A.4)


                        (t2 + k )(3t2 − k )(1 − λ ) λ (t2 − k )2 1 (t2 + k ) 
                       
                                                  2
                                                    + 2             −
                                                                   2          
                                    8t 2                   2t 2       4t1    when t ≥ k
                                       (1 + λ )(t2 + k )(3t 2 − k ) 
                                                                                       2

                                      1−        2
                                                                      
                                                   16t1t2           
                  rN = 
                       
                       
                       
                        2t1t2 (1 − λ )2                                         when t2 < k
                       [t1 − t2 (1 + λ )]
                       4                 2




             it ing        o          ds h h
        Subst ut (A .4) int (A.3) yie l t at t e s urpl in t e negot ions w it Ne t
                                                      us    h       iat       h    scape is
     iv
posit e (i.e ., D > 0) if:

          (t 2 + k )(3t 2 − k )  (t 2 + k )(3t 2 − k )  (t 2 − k ) 2    (t 2 + k )  (t 2 + k )(3t 2 − k ) 
                                −
                                 1                      −               1 −
                                                                                     1 −                    > 0
                 32t 2                  8 t1 t 2           16t 2            2t1          16t1t 2        
                                                                                                               
w h e n t 2 ≥ k and
                                               t2    4 t1 − 2 t 2       
                                                                        > 0
                                               8    4t1 − t 2 (1 + λ2 ) 

w h e n t 2 < k . It is negat e ot e rw is e . Th e re gions spe cified in t e O bserv ion fol from t e
                             iv h                                           h         at     low     h

    e
abov e xpressions.         Q.E.D .


                 ion
Proof of Proposit 1
        Se t ing t e diffe re nce ∆ = rT − rW so t at D = 0 yie l
            t     h                               h             ds:


W h e n t2 ≥ k

            1 (t 2 + k )(3t 2 − k )  rN (t 2 + k )(3t 2 − k ) (t 2 + k )(3t 2 − k )t1 (t 2 − k ) 2    1 t 2 + k 
  (rT − rW ) −
            4                       =
                                      2                       −                       +                 −
                                                                                                        2         
                     64t1t 2                   32t1t 2                32t1t 2             8t 2             4 t1 
                                                                                                                   


and w h e n t 2 < k :




                                                             35
                                     (rT − rW )  t 2  rN t 2 t 2
                                                 4t  = 16t − 8 .
                                                1 −   
                                         4          1      1




Subst ut for (rT − rW ) int e q uat
     it ing                o                              ds h     ut                             h
                                   ions (17) and (18) yie l t e s ol ion for rN as spe cified in t e

Proposition.
             h                     ion        low h h            s                     e
       From t e first orde r condit (12) it fol s t at t e profit of M icrosoft are giv n by
                                                                                                      (A.5)
                                             rT + rW         r
                                      M =            = p S − N − t1 ,
                                                2             2


               v           ion         it ing         o           ds                        h
w h e re p S sole s e q uat (13). Subst ut for p S int (A .5) yie l M icrosoft's payoff at t e

        usionary e q uil
non-e xcl              ibrium .    Q.E.D .


                 ion
Proof of Proposit 2
       W h e n Ne t               osed from t e m ark e t t e disagre e m e nt payoff of M icrosoft in t e
                   scape is fore cl          h             h                                            h
      iat       h         ure
ne got ions w it m anufact rs i ch ange s from (6) to


                                              v t    pj 
                                        M * =  − 2 − S rTj ,
                                              t 2t
                                              1    1 t1 
                                                         


                                                ed ransport ion cost giv n t e reduced ch oice am ong
since e ach consum e r incurs h igh e r e xpe ct t         at       s   e h
                     ut
brow s e rs. Th e s ol ion for p S is obt       e        arl o h        at
                                         ained v ry sim il y t t e deriv ion in (13). Th e

m odificat             ied   h                                              h        h            iat
          ions are im pl by t e diffe re nt disagre e m e nt payoff M *and t e fact t at no ne got ions
w it Ne t
    h    scape t e pl s o t at rN = 0. Th e profit of M icrosoft are obt
                ak  ace    h                      s                     ained from (12) by

     it ing rN = 0.
subst ut               Q.E.D .


                 ion
Proof of Proposit 3
            low                                                w
       It fol s by direct com parison of th e payoffs of th e t o pre vious propositions.




                                                    36
                 ion
Proof of Proposit 4
                                t h             usionary e q uil
        Th e profit of M icrosof at t e non-e xcl                           e
                                                               ibrium is giv n by:



                                                                           r  (1 − λ ) 2
                                                                                2
                                t2            r           t2
                               v −   − 2 t1 − N     +    v −   − 2 t1 − N  +      1
                                                                                        4 t1
                                   4           2             4           2   2λ
                      M NE =                                                        1
                                                                                             .
                                                                2


    h    icit  usionary cl
W it e xpl e xcl                h            s
                         auses t e s e profit ch ange to:



                                                                          (1 − λ ) 2
                                                                         2
                                     t2                   t2
                                    v −   − 2 t1  +      v −   − 2 t1  +      1
                                                                                    4 t1
                                        2                    2           2λ
                           ME =                                                 1
                                                                                         .
                                                                2


It is e asy t dem onst e t at M NE > M E prov
             o        rat h                  ided t at rN < t 2 / 2. Th e expressions deriv for rN
                                                   h                                       ed

are s m al r prov
         le      ided t at t 2 is sm al and/or λ is l .
                       h              l         2   arge              Q.E.D .


          em
Proof of L m a 3
        O bt            im             h            o i                it ion          ry
            ained by opt izing S i w it re s pe ct t p S and upon subst ut of sym m e t and (20).

Q.E.D .


                 ion
Proof of Proposit 5
W h e n t2 ≥ k


                                        v t    p i  (r i − r i ) (t + k )(3t 2 − k )( p S − rTi )
                 [−                   ]
                                                                                          i
                 S     S i* + N − N * =  − 2 − S  T W + 2
                                         t 4t  t1  2
                  i
                                        1    1                             16t1t 2



                                         (t 2 − k )2  v
                                                     
                                                         p S t 2 3(t 2 + k )
                                                           i
                                                                            
                                     −              t − t − 4 t −
                                             8      1    1     1    8 t1  




                                                            37
     it ing       ry      l h                        ed   e           ds:
Subst ut sym m e t as w e l as t e e xpression de riv in L m m a 3 yiel


                                      v t    r  λ ∆ (t 2 + k )(3t 2 − k ) λ  t 2 
              [−
              S  i               ]
                     S i* + N − N * =  − 2 − N  1
                                      t 4t 2t 1 + λ 2 +                  1 + λ v − 4 
                                                                                1

                                      1   1   1    1       16t1t 2             1     



                                    ∆  (t 2 − k )     v t 2  rN  λ     3(t 2 + k )
                                                  2
                            rN
                       +          +     −              t 4t − 2t 1 + λ −
                                                       −                            ,
                                                                       1

                         2(1 + λ ) 2 
                                1          8t 2       1    1
                                                                    
                                                                  1     1     8 t1 



w h e re ∆ = (rT − rW ).


        Th e abov com bined surpl is t e s m al s t w h e n ∆ = 0 . H ow e v r, e v n t e n t e s urpl
                 e              us    h       le                            e      e h       h       us
     rict y  iv                  e           ibrium w it posit e m ark e t sh are s for e ach
is st l posit e (assum ing an int rior e q uil          h     iv
produce r.)


W h e n t2 < k


                                                v t    p i  (r i − r i ) t
                        [−
                        S  i                 ]
                               S i* + N − N * =  − 2 − S  T W + 2 ( p S − rTi ),
                                                t 4t        2
                                                                                i

                                                1   1  t1                4 t1


w h ich is, once again, st l posit e e v n w h e n ∆ = 0 .
                          rict y  iv e                                                          Q.E.D .


                 ion
Proof of Proposit 6
            h                 usiv y auses, M icrosoft's profit are giv n from L m m a 3 as:
        In t e absence of e xcl it cl                          s       e        e


                                                                        2
                                              2λ (1 − λ )  t 2 rN 
                                      M NE   = 1         1
                                                            v −  −  ,
                                              t1 (1 + λ ) 2 
                                                       1         4 2 


                                      o        usion.
w h e re s ubscript NE corre s ponds t non-e xcl




                                                        38
           h    icit  usiv y   ract h    low        h
       W it e xpl e xcl it cont s, t e fol ing are t e agre e m e nt and disagre e m e nt
            h        iat      w                              ure
payoffs in t e ne got ions bet e e n M icrosoft and m anufact r i:


                                    v t     p i R(t 2 , k ) i
                               Si =  − 2 − S −
                                     t 4t                  ( p S − rTi )
                                    1     1 t1     t1     


                      v t    p i R (t 2 , k ) i  v t 2     p j R (t 2 , k ) j
                   M = − 2 − S −
                      t 4t                   rT +  −     − S −             rT
                      1   1  t1      t1     
                                                    t 4t
                                                    1    1   t1      t1     


                                                      S i* = 0



                                      v t    p j R (t 2 , k ) j
                                 M* =  − 2 − S −
                                      t 4t                   rT
                                      1    1 t1      t1     


                       ut       isfie
Th e Nash Bargaining Sol ion sat s :


                                  (1 −   λ )(S i − S i* )− λ (M − M * )= 0
                                          1                 1




       oge h      h h     im   ion
Th is t t e r w it t e opt izat of S i w it re s pe ct t p S yie l at t e sym m e t e q uil
                                           h            o i      ds    h           ric    ibrium :



                                   rT =
                                           (1 −   λ ) t 2                   
                                                            − t1 R (t 2 , k )
                                                   1
                                                     v −
                                           (1 +   λ )
                                                   1      4                  


          s o                      t
and profit t M icrosoft are e q ual o:


                                    2λ (1 − λ )  t 2
                                                                                 2
                                                                    
                                ME = 1        1
                                                v − 4 − R(t 2 , k ) .
                                    (1 + λ ) t1 
                                          1
                                            2
                                                                    


             ion l
                 ow                        h
Th e Proposit fol s by com paring M NE w it M E .                   Q.E.D.


                                                        39

								
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