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					                    Game Theory



“Life must be understood backward,
  but … it must be lived forward.”
         - Soren Kierkegaard




                               Mike Shor
                               Lecture 4
Review
   Recognize dominant and
    dominated strategies
   Dominant strategies are always played
   Dominated strategies are never played


   Equilibrium: likely outcome of a game
       • Dominance solvable
       • Iterated deletion of dominated strategies


                   Game Theory - Mike Shor           2
Cell-by-Cell Inspection
   Games of Assurance
      • The “good” equilibrium is risky
      • Need assurances
   Games of Coordination
      • Failure to agree leads to no profits
      • Can’t agree on “what to agree on”
   Games of Chicken


                   Game Theory - Mike Shor     3
  Games of Chicken
      A monopolist faces a potential entrant
      Monopolist can accommodate or fight
      Potential entrant can enter or stay out

                              Monopolist
                  Accommodate               Fight
Potential
Entrant




            In      50 , 50               -50 , -50
            Out      0 , 100                0 , 100

                     Game Theory - Mike Shor          4
Equilibrium
   Use best reply method
    to find equilibria
                                 Monopolist
                  Accommodate                  Fight
Potential
Entrant




            In      50 , 50                  -50 , -50
            Out      0 , 100                   0 , 100



                   Game Theory - Mike Shor               5
Importance of Order
   Two equilibria exist
      • ( In, Accommodate )
      • ( Out, Fight )
   Only one makes temporal sense
      • Fight is a threat, but not credible
      • Not sequentially rational
   Simultaneous outcomes may not
    make sense for sequential games.

                   Game Theory - Mike Shor    6
Sequential Games
       The Extensive Form

               0 , 100
   E
                               -50 , -50
          M


                               50 , 50

            Game Theory - Mike Shor        7
Looking Forward…
   Entrant makes the first move:
      • Must consider how monopolist will respond
   If enter:                         -50 , -50
                 M


                                      50 , 50

   Monopolist accommodates

                  Game Theory - Mike Shor         8
… And Reasoning Back
   Now consider entrant’s move
                                 0 , 100
      E

              M
                     acc
                                 50 , 50


   Only ( In, Accommodate ) is
    sequentially rational
               Game Theory - Mike Shor     9
Sequential Rationality

            COMMANDMENT
    Look forward and reason back.


   Anticipate what your rivals will do
               tomorrow
      in response to your actions
                 today



              Game Theory - Mike Shor    10
Solving Sequential Games
 Start with the last move in the game
 Determine what that player will do
 Trim the tree
    • Eliminate the dominated strategies
 This results in a simpler game
 Repeat the procedure




                Game Theory - Mike Shor    11
Voting Revisited
   Majority rule results:
       • B beats G   ;    G beats R            ;   R beats B
   What if you want “Remand” to Win?
       • B vs. G then winner vs. R                    R
   Problem:
       • Everyone knows you want “R”
         B vs. G then winner vs. R? Good Luck!
       • Better chance:
         R vs. G, then winner versus B


                     Game Theory - Mike Shor                   12
Extensive Form
                                      B
          B vs. R


R vs. G                               R

                                      B


          B vs. G
                                      G
            Game Theory - Mike Shor       13
Looking Forward
          B
B vs. R
                  A majority prefers R to B

          R

          B

                   A majority prefers B to G
B vs. G
          G
          Game Theory - Mike Shor             14
Trim The Tree

          B vs. R


R vs. G                               R

                                      B


          B vs. G

            Game Theory - Mike Shor       15
Reasoning Back
   First stage, in effect vote between R & B
   Gore supporters prefer G>R>B, vote R

                  B vs. R

      R vs. G                               R

                                            B


                  B vs. G
                  Game Theory - Mike Shor       16
What Happened?
   Gore supporters have preferences
        •Gore > Remand > Bush
   In first round, vote between R and G
   Gore supporters prefer Gore
    But vote for G is in effect a vote for B!
   So Gore supporters vote for remand.
    Guarantee themselves second best choice


                 Game Theory - Mike Shor   17
Rollback in Voting and
“Being Political”
   Not necessarily good to vote
    your true preferences
   Amendments to make bad bills worse
   Crossing over in open primaries
   “Centrist” voting in primaries
   Supporting your second-best option
   STILL – Outcome predetermined
   AGENDA SETTING!

                Game Theory - Mike Shor   18
Predatory Pricing
   An incumbent firm operates in three
    markets, and faces entry in each
      • Market 1 in year 1, Market 2 in year 2, etc.

   Each time, I can slash prices, or
    accommodate the new entry
   What should I do the first year?


                  Game Theory - Mike Shor        19
     Predatory Pricing

              E2                         E3



E1

        M                   M



               Game Theory - Mike Shor        20
Predatory Pricing
    The end of the tree: year 3
              0 , 100 + previous
E3
                           -50 , -50 + previous
          M


                           50 , 50 + previous
    In year 3: ( In, Accommodate )
                  Game Theory - Mike Shor         21
     Rollback
        Trim the tree:
                  E3          M acc
                        in                0 , 100 + previous


E2
                         in      acc
                                        -50 , -50 + previous
            M

                          in     acc
                                             50 , 50 + previous
                       Game Theory - Mike Shor              22
Predatory Pricing
 Since the Incumbent will not fight
  Entrant 3, he will not fight Entrant 2
 Same for Entrant 1
 Only one “Rollback Equilibrium”
      • All entrants play In
      • Incumbent plays Accommodate
   Why do we see predatory pricing?


                 Game Theory - Mike Shor   23
       Game Theory


   Example

Sequential Entry
Market Opportunity Analysis

   “Assesses the potential of a
geographic market for a specific set
of products, providing a
prioritization of market coverage
voids and recommending market
entry strategies.”


             Game Theory - Mike Shor   25
   “Market Analysis”


                                       700
                                       SBCs
400
SBCs




             Game Theory - Mike Shor      26
Extended Market Analysis
   If enter 400 SBC market:
     Next entrant, to break even,
      must expect market share of 300/400
     Must expect market share of 75%

   If enter 700 SBC market:
     Next entrant, to break even,
      must expect market share of 300/700
     Must expect market share of 43%

   Real decision:
       All of 400 or half of 700
                    Game Theory - Mike Shor   27
Breakfast Cereals
                               vertical axis:
                               sales (in thousands)
 600

 500
                               product development costs:
                               $1.2M per product
 400

 300

 200

 100

 000

        1   2   3   4      5    6    7    8       9    10     11
       less                                           more
       sweet                                          sweet
                        Game Theory - Mike Shor                    28
                                                                  1
First Product Entry
                              Profit = ½ bh – F

 600
                                       = ½ 5(600) – 1200
 500                                   = 1500 – 1200
 400
                                       = 300
 300

 200

 100

 000

        1      2   3   4     5    6    7    8    9    10     11

       less                                          more
       sweet                                         sweet
                           Game Theory - Mike Shor                    29
                                                                  2
Second Product Entry
                  Profit = 2 x 300

600
                           = 600
500

400

300

200

100

000

       1      2    3   4     5    6    7    8    9    10     11

      less                                           more
      sweet                                          sweet
                           Game Theory - Mike Shor                    30
                                                                  3
Third Product Entry
                  Profit = 600 + 1500 – 480 – 1200

600
                           = 420
500

400

300

200

100

000

       1      2    3   4     5    6    7    8    9    10     11

      less                                           more
      sweet                                          sweet
                           Game Theory - Mike Shor                    31
                                                                  4
Competitor Enters
                  Profit = 600 - 240

600
                           = 360
500

400

300

200

100

000

       1      2    3   4     5    6    7    8    9    10     11

      less                                           more
      sweet                                          sweet
                           Game Theory - Mike Shor                    32

				
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posted:10/17/2011
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