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Theory of Moves


									Theory of Moves

Adding n dynamic dimension to game theory allows players to look ahead
before making moues, thereby                               ueating a mlre renlistic game

Steven J. Brams

J-\uring        the Cuban missile crisis jn               Game theory approaches conflicts by            These modifications lead to different
l-zt      October 7962, the Kennedy admin-             asking a question as old as games them-        stable outcomes, or equilibria, from
istration demanded that the Soviet                     selves: How do people make "optimal"           those of classical game theory and new
Union remove its missile bases from                    choices when these are contingent on           concepts of power. In this article, I shall
Cuba. The Soviets acquiesced, but only                 what other people do? The seminal              describe informally ideas underlying
after the world teetered for days be-                  work was done in the 1940s by mathe-           the theory of moves and illustrate some
tween peace and disaster. Theodore C.                  maticianlohn von Neumanrt and econ-            of its concepts in several games-the
Sorenson, special counsel to President                 omist Oskar Morgenstern, both of               last being one that models the Iran
Kennedy, later recalled, "We discussed                 Princeton University, who discovered           hostage crisis that began tn 1979.
what the Soviet reaction would be to                   that they held similar ideas about strate-
any possible move by the United States,                gies in games. They realized, first, that      Making Moves
what our reaction with them would                      strategies are interdependent: Players         Before considering the theory of moves,
have to be to that Soviet reaction, and so             cannot make unilaterally optimal deci-         it is worth noting some basic elements
on, trying to follow each of those roads               sions, because one player's best choice        of classical game theory. Von Neumann
to their ultimate conclusion."                         depends on the choices of other play-          and Morgenstern defined a game as
   The Cuban missile crisis is a classic,              ers. Von Neumann was responsible for           "the totality of ruies of play which de-
albeit high-stakes, example of strategic               most of their theoretical work, whereas        scribe it," which includes a starting
game-playing. Like chess players,                      Morgenstern pushed the applications            point and a list of legal moves that play-
world leaders in conflict situations                   toward economic questions.                     ers can make. The game of tic-tac-toe,
make carefully considered moves and                      Their collaboration led to a monu-           for example, begins when one player
countermoves. But the outcomes are not                 mental and difficult treatise, Tlrcory of      makes a mark on a three-by-three
always what the players or onlookers                   Games and Economic Behaaior (7944),            board. The rules state that a player can
expect; in particular, it is sometimes                 which was revised in 1.947 and then            mark either an X or an O, but only in an
hard to understand why players choose                  again in 1953. Over the next several           unmarked block. After the first player
conflict over cooperation.                             decades investigators applied game the-        makes a mark, the second player does,
   A body of theory, called game theory                ory to strategic situations ranging from       with the players then alternating in
has been developed and applied over                    the evolution of animal behavior to the        making marks on the board. The game
the past half-century to analyze mathe-                rationality of believing in God.               ends when one player gets three marks
matically the strategic behavior of peo-                 According to the classical theory,           in a row or all the blocks are filled.
ple in situations of conflict. The theory              players choose strategies, or courses of          Most games can be described in two
facilitates reconstruction of past situa-              action, that determine an outcome. Von         different ways. The "extensive form" is
tions and modeling of possible future                  Neumann and Morgenstem called their            given by a game tree, with play begin-
ones, which can explain how rational                   theory "thoroughly static" because it          ning at the first fork in the tree. One
decision makers arrive at outcomes that                says little about the dynamic processes        player selects one side of this fork,
are often puzzhng at first glance.                     by which players' choices unfold to            which moves the game to another fork.
                                                       yield an outcome.                              Then the other player selects a side of
                                                          I have developed what I call the "the-      that fork, and so on until the game ends.
Stez:en  l. Brams is professor of politics at New      ory of moves" to add a dynamic dimen-          This form of a game provides a full de-
York Unittersity, iohere he lns tnught since 1969.     sion to classical game theory. Like the        scription of its sequentiai moves.
He is the autlrcr or coauthor of 17 books thnt                                                           By contrast, the "normal form" is giv-
                                                       classical theory the theory of moves fo-
hnolae npplications of game theory or social-
                                                       cuses on interdependent strategic situa-       en by a payoff makix, in which players
choice theory to ztoting and elections, interrntion-
                                                       tions in which the outcome depends on          choose strategies simultaneously o4 if
al relations, the Bible and theology. Theory of
Moves, the book on zuhich this article is based,       the choices that all players'make. But it      not, at least independently of each other.
will be published by Cambridge Uniuersity Press        radically alters the rules of play, enabling   (A strategy gives a complete plan of
in lanuary. Address: Department of Politics,           players to look ahead-sometimes sev-           possibly contingent choices-if you do
New York Uniaersity, Nezu York, NY 10003.              eral steps-before making a move.               this, I will do that, etc.) Thus, if a game

562       American Scientist, Volume   81
 *it      *|
  ?        -r;"


        Figure 1. Game theory evaluates behavior in conflict sifuations. During the Cuban missile crisis, President Kennedy demanded that the Soviet Union re-
        move its missiles from Cuba. Kennedy and his advisors, shown here in an Excom (Executive Commiftee) meeting considered all their possible moves, the
        possible countermoves by the Soviets and the possible counter<ountermoves by the United States. U.S. decision makers used their knowledge of the past
        and predicted future moves, which classical game theory tends to treat myopically. The author's theory of moves adds a dynamic component to classical
        game theory enabling players to look ahead and select shategies that yield "nonmyopic equilibria." (Photograph courtesy of the John E Kennedy Library.)

        has two players, each     with two possible        games become quite intractable after just           and present as well as the future, which
        strategies,   it can be represented by        a    a few moves, although in principle the              players can anticipate at least in part
        two-by-two payoff matrix. One player's             theory of moves is applicable to rt-per-            and about which        I   assume they can
        strategy choices are given by the two              son games in which each of the n play-              make rational calculations.
        rows; the other's are given by the two             ers has a finite number of strategies.                 In the theory of moves, I assume that
        columns. Each row-and-column inter-                   Beyond the structure of a game (nor-             players can rank the possible outcomes
        section defines an outcome, where pay-             mal or extensive form), one can make                from best to worst. These payoffs, how-
        offs are assigned to the two players.              other modifications in the definition of            ever, are only ordinal: They indicate an
           The theory of moves combines the ex-            what constilutes a rational choice. A ra-           order of preference, but not the degree
        tensive and normal forms of classical              tional choice depends on, among other               to which a player prefers one outcome
        game theory. A theory-of-moves game                things, hon, far players look ahead as              over another. (Although other forms of
        is played on a payoff matrix, like a nor-          they contemplaie each other's possible              decision-making theory indicate the de-
        mal-form game. The players, however,               moves and countermoves. In addition,                gree of preference in payoffs, I have cho-
        can move from one outcome in a payoff              moves are influenced by the capabilities            sen ordinal payoffs to simplify the
        matrix to another, so the sequential               of the players and their information               anaiysis and make it more applicable to
        moves of an extensive-form game are                about each other.                                  real-life strategic situations.) In addition,
        built into the more economical normal                 The theory of moves incorporates all            the theory allows for power differences
        form. In large part, I shall concentrate on        these features. It is dynamic because              among players by assuming, for exam-
        two-player games in which each player              players do not make choices de nouo.In-            ple, that one player may have the ability
        has two strategies; more complicated               stead, their choices depend on the past            to carry out threats when necessary. Fi-

                                                                                                                        1993    November-December
                                                                                                        the only point at which the players ac-
                                                                                                        crue payoffs.
                                                                                                           The remaining rules, which I call ra-
                                                                                                        tionality rules, explain the reasons for
                                                                                                        moving or not moving. Rule 5 states
                                                                                                        that a player will not make a move un-
                                                                                                        less   it   leads to a preferred outcome/
                          op{ion   1                              optron 2                              based on his or her anticipation of the fi-
                                                                                                        nal state. Rule 6, which I call the two-
                                                                                                        sidedness rule, says that a player con-
                                                                                                        siders the rational calculations of the
                                                                                                        other players before moving, taking into
                                                                                                        account their possible moves, the possi-
                  player B                                           player B                           ble countermoves of the other players,
                                                                                                        their own counter-countermoves, and
                                                                                                        so on. Thus, a player may do immedi-
                                                                                                        ately better by moving first according
  option                           option Z                                                             to Rule 5; but if this player can do even
                                                                                                        better by letting the other player move
                                                                                                        first, and it is rational for that player to
                                                                                                        do so, then the first player will await
  outcome                    outcorne 2                outcome 3                 outcorne      4        this move, according to Rule 6.

Figure 2. Extensive form of classical game theory is given by a game tree. This game involves two       Some of the differences between classi-
players, with each player able to choose one of two options. The game begins when Player A se-          cal game theory and the theory of
lects an option, Then Player B selects an optiory which leads to one of four possible outcomes.         moves arise in an imaginary confronta-
This form highlights the sequential nature of moves.                                                    tion situation called a truel. A truel is
                                                                                                        like a duel, except there are three play-
                                                       playeF        B                                  ers. It illushates nicely the applicability
                                                                                                        of the theory of moves to games with
                                                                                                        more than two players.
                                        strategy   1                     strdtegy       2                  In the truel I posit, a player has two
                                                                                                        choices: either to fire or not to fire at one
                                                                                                        of the other two players. Each player
                    r                  oqtcorne                          oulcome
                                                                                                        has one bullet and is a perfect shot. The
                    cr)                                                                                 players cannot communicate, which
                                        (x,,Y,)                           (   x,,y.)                    prevents the selection of a common tar-
                                                                                                        get. I assume that a player's primary
                                                                                                        goal is to survive, and his or her sec-
player A                                                                                                ondary goal is to survive with as few
                    N              oqtcorne 2                            outCorn€ 4                     other players as possible.
                    ul                                                                                      In this rather gruesome situation, the
                    +r                 (xr., y1)                         (xa,/r)                        theory of moves suggests a different
                                                                                                        outcome than does classical game theo-
                                                                                                        ry. In fact, the theory of moves provides

                                                                                                        a resolution that is more satisfactory for
Figure 3. Normal form of classical game theory is given by a payoff matrix. In a two-player game in     all the players.
which each player has two strategies, the matrix is two-by-two. Player ,{s strategies are represent-        If the players must make simultane-
ed by the two rows, and Player B's are represented by the two columns. Players independently se-        ous strategy choices, they will all fire at
lect strategies that lead to an outcome. Each outcome is assigned payoffs, which are given in x-y       each other according to classical game
combinations such that x; is the payoff to the row player (Player A) and y; is the payoff to the col-   theory. They do so because their own
umn player (Player B), where i and I are given by the players' shategies (either 1 or 2).
                                                                                                        survival does not depend one iota on
                                                                                                        what they do. Since they cannot affect
nally, the theory is information-depen- Rule 2 says that either player can switch                       what happens to themselves but can af-
dent, meaning that players do not al- to a new strategy, thereby generating a                           fect only how many others survive (the
ways share the same informatiory mak- new outcome; the fust player to move is                           fewer the bettel, according to the pos-
ing misperception and deception called Player 1. According to Rule 3, the                               tulated secondary goal), they should all
possible.                                   other playeq, Player 2, can then move.                      fire at each other.
   The theory of moves includes six ba- A game's end is determined by Rule 4:                              Such a scenario generates two possi-
sic rules. Rule 1 states that a game starts The players respond alternately until                       ble results: Either one player survives
at an "initial state," which is a row-and- neither switches strategies. The result-                     or no players survive. Players A and B
column intersection of a payoff matrix. ing outcome is the "final state," which is                      mightboth fire at Player C, who fires at

564   American Scientist, Volume 81
one of them, say Player A. This leaves a                                                              player       B
single survivor, Player B. On the other
hand, each player may fire at a different
player, leaving all players dead.
                                                                                     strategy    1                     StrategY 2
   If each player has an equal probabili
ty of firing at one of the other two play-                           f              outcome      1                     outcome 3
ers, there is only a 25 percent chance
that any player will survive. The reason
is that Player A will be killed if fired at
by Player B, Player C or both (three cas-
                                                                                     (x,,,Y,)           #w              ( xr,/r)

es); the only case in which Player A will
                                                                                        m                                "*x.
survive is if Players B and C fire at each
                                                 player A
                                                                                     it*                                   t
other, which gives Player A one chance                               ^j            outcorne a                          outcome.    4
in four of surviving. Although this cal-
culation implies a 75 percent chance
                                                                                     (Y,Y,) n # e,,y,)
that some player will survive, an indi-
vidual player will be more concerned
with his or her own low chance (25 per-
cent) of survival.                              Figure 4. Theory of moves embeds a game tree in a payoff matrix. Players can move from an ini-
   The theory of moves offers a different       tial outcome or state to another one by either moving vertically (Player A) or horizontally
perspective. lnstead of assuming simul-         er B). The matrix shows the strategies of the players and their payoffs at various outcomes. The
ianeous strategy choices, it asks each          arrows within the matrix reveal how players might move-in this case counterclockwise-be-
player: Given your present situation and        tween different outcomes through a sequence of moves.
the situation that you anticipate will en-
sue if you fire first, should you fire? At         \A/hat classical game theory does not             then Players B and C will shoot each
the start of a truel, all the players are       ask is whether it is rational for one play-          other. The disarmed Player A is, after
alive, which satisfies their primary goal       er, if afforded the opportunity, to move             all, no threat, so he or she would not be
of survival but not their secondary goal        first. This is specified by the rules in the         shot by Player B or Player C. On the
of surviving with as few others as possi-       classical theory instead of being made               other hand, Players B and C will fire im-
ble. Player A now contemplates shoot-           endogenous-that is, incorporated into                mediately at each other; otherwise, they
ing Player B to reduce the number of            the theory as a question to be an-                   wiil have no chance of surviving to get
sun.ivors. Bv looking ahead, hott'ever,         su'ered-as in the theon'of moves.                    in the last shot. In the end, Plaver A will
Player A realizcs ihat firir"rg ai Piaycl D        Ch..ngiiig tlie lulcs oi play may      terr       be il-ie sole survivor under these rules
will cause Player C subsequently to fire        erate still different outcomes. For exam-            that give a player the option of firing in
at him or her (Player A). This would be         ple, permit the players of a truel the ad-           the air.
in Player C's interest, because it would        ditional option of firing in the air,
make C the sole survivor.                       thereby disarming themselves, and                    Prisoners'Dilemma
   hstead of firing, therefore, Player A        specify the order of play, such as Player            Game theory's most famous game is
will, thinking ahead, not shoot at any-         A goes first, foliowed by Players B and              called Prisoners'Dilemma. It starts with
body. By symmetry, the other players            C going simuitaneously. Given these                  the following scenario: Two persons,
will choose the same strategy, so all will                    will fire in the air, and
                                                rules, Player A                                      suspected of being partners in a crime,
survive. This longer-term perspective
leads to a better outcome than that pro-
vided by classical game theory, in which
each player's primary goal is satisfied
 orly 25 percent of the time when play-
ers make simultaneous strategy choices
without looking ahead.
   The purpose of the theory of moves,
however, is not to generate a better out-
come but to provide a more plausible
model of a strategic situation that mim-
ics what people might think and do.
The players in a tn-rel, artificial as such a
shoot-out might be, would be motivat-
ed to look ahead, given the dire conse-                                        c
quences of their actions. To be sure, clas-
Jical game theory can also provide this         Figure    Tiuel is a three-person duel. Here each player is assumed to have a single bullet and be
outcome if one player (say, A) were des-        a ierfect shot. A playerCprimary goal is surviving and the secondary goal is surviving
                                                                                                                                           with as
 ignated to move first. Then Player A           few others u, pogibi". If ihe players must make simultaneous choices, a player cannot affect his
 would rationally choose not to fire, lest      or her own survival but can iffect how many others survive; consequently, each player is moti-
 he or she be killed subsequently by the        vated to shoot another. Classical game theory indicates two possible outcomes: either no one sur-
 sole surwiving player (either B or C).         vives (Ieft),or one player-Player B in this case-suwives iight)'

                                                                                                              1993 November-December           565
                                                                                                   Iran Hostage Crisis
                                                                                                   Although a rational player should look
                                                                                                   ahead before acting, that advice works
                                                                    Khorneini                      well only if the players have complete
                                                                                                   information about their opponents.
                                                                                                   The United States apparently lacked
                                                                                                   such information about Iran in No-
                                  negot tat ion                      obstuction                    vember 7979, when Iranian militants
                                                                                                   seized personnel at the U.S. embassy.
                                                                                                   By analyzing the news reports of the
                                 cornprom r5e                    Carter Surrenders                 time and the later writings of some
                                                                                                   government officials, Walter Mattli of
                                                                                 4                 the University of Chicago and I recon-
                                                                                                   structed the strategic thinking of deci-
                               ffi &    &
                                                                        ,. .r7
                                                                                                   sion makers in this crisis. As I shall
                                                                                                   show, it explains well why the crisis
                     c         Khomeini surrenders                    qlsaster                     took so long to resolve.
                  >..;                                                                                During the crisis, the military capa-
 Carter           ,uI

                  {J>                        7
                                                            'f&r                                   bilities of the two opponents were al-
                 -_ aJ
                   -c                                         M                                    most irrelevant. ln April 1980 ihe Unit-
                                                                                                   ed States attempted a rescue that cost
                                                                                                   eight American lives and freed no
                                                                                                   hostages, but the conflict was never re-
                                                                                                   ally a military one. The crisis canbebest
Figure 11. Carter apparently misperceived the structure of the Iran hostage crisis by believing
                                                                                                   represented as a game in which Presi-
that Khomeini prefened compromise to a confrontation that Carter thought might end in a dis-
                                                                                                   dent |immy Carter misperceived the
aster. Carter's misperceived payoff matrix shows that he gets a better payoff by selecting ne-
gotiation, regardless of Khomeini's choice. According to this payoff matrix, Khomeini's best       preferences of Ayatollah Ruholla
strategy depends on Carter's selection. If Carter selects military intervention, Khomeini should   Khomeini. In desperation, Carter
select negotiation. If Carter selects negotiatiory Khomeini should select obstruction, resulting   sought a solution in the wrong game.
in the outcome called "Carter surrenders," which is the equilibriurn outcome (blue). ll the           Why did Khomeini sanction the
players moved and countermoved around the matrix, the moves would be clockwise, because             takeover of the American embassy by
in that direction no player ever moves from his best payoff.                                       militant students? Doing so provided
                                                                                                    iivo aciv aniages. First, by cleatiilg a con-
                                                                                                   frontation with the United States,
                                                                                                   Khomeini was able to sever the many
                                                                                                   links that remained between Iran and
                                                                                                   the "Great Satan" from the days of the
                                                                   Khomeini                        shah. Second, the takeover mobilized
                                                                                                   support for extremist revolutionary ob-
                                                                                                   jectives just at the moment when secular
                                                                                                   elements in Iran were challenging the
                                 negotialton                        obstruction                    principles of the theocratic state that
                                                                                                   Khomeini had installed.
                        c       Carter succeed5                Khomeini succeeds                     Carter's primary goal was immedi-
                        o                                                                          ate release of the hostages. His sec-
                                                                       2" 4                        ondary goal was holding discussions
                                                                                                   with Iranian religious authorities about
                       A)                                                                          resolving the differences that had
                        c                                                                          strained relations between the United
                                                                                                   States and Iran.       Of course, if the
                           I   Carter    adarn ant             Khome'ni:adanr ant                  hostages were killed, the United States
                  >rH                                                                              would likely defend its honor, probably
Cart€r            ro \g                                                                            through a military strike on Iran.
                  ;AJ                                                                                 Carter considered two strategies: ne-
                    c                                                                              gotiation and military intervention. Be-
                                                                                                   cause the seizure of the embassy had
                                                                                                   1ed to a severing of diplomatic relations,
Figure 12. Real-game payoff matrix, taking into account Iran's internal politics as revealed by
                                                                                                   negotiation could be pursued only
events and analysis, shows that Khomeini has a dominant strategy of selecting obstruction,
which is better for him regardless of Carter's strategy. Like the misperceived-game payoff ma-
                                                                                                   through the United Nations Security
trix (Figure 11), Catler has a dominant strategy of selecting negotiation. These strategies lead   Councii, the World Court or informal
again to a negotiation-obstruction outcome, which is an equilibrium outcome (blue), now            diplomatic channels. Military interven-
called "Khomeini succeeds" because Khomeini ranks the other outcomes differently than in           tion could have taken the form of a res-
the misperceived-game payoff matrix. Cycling in this matrix would be clockwise.                    cue mission, as it did, or punitive strikes

568   American Scientist, Volume    81
    against selected targets, such as refiner-
    ies, rail facilities or power stations.
       Khomeini also had two strategies: ne-
gotiation or obstruction. His negotiating
demands included a retum of the shah's
assets and ending U.S. interference in
Iran's affairs. On the other hand, a re-
fusal to negotiate was sure to block a
resolution of the crisis.
   The two players and their two strate-
gies generate a two-by-two payoff ma-
trix. Each cell in the matrix has an asso-
ciated payoff for each player. As in
Prisoners' Dilemma, I assume that
Carter and Khomeini can rank the four
outcomes frombest (4) to worst (1).
  Carter obtains a better payoff by
choosing negotiation, which would
save him from the overwhelming diffi-
culties of military intervention, whatev-
er Khomeini does. In December 1979
those difficulties were compounded by            Figure 13. Carter tried military intervention even though negotiation was his dominant shategy in
the Soviet invasion of Afghanistan,              both games. The attempted rescue mission left one U.S. helicopter destroyed and another aban-
                                                 doned. Classical game theory makes such a strategy appear irrational in both game makices,
which eliminated the Soviet Union as a
                                                 whereas the theory of moves offers a rational explanation for Carter's action. In the misperceived-
possible ally in seeking concerted action
                                                 game matrix (Figure 11), Carter believes that selecting military intervention--or threatening its
for the release of the hostages. More-           use-will force Khomeini to select negotiation in order to improve his payoff, at which point
over, the Soviet troops next door in             Carter can also choose negotiation to obtain his best payoff at the "compromise" outcome, which is
Afghanistan made the strategic envi-             also better for Khomeini. In the real-game payoff matrix (Figte 12),I{homeini cannot be swayed
ronment for military intervention any-           ftom obstruction. The crisis, in fact, remained at a negotiation-obstruction outcome until the
thing but favorable.                             hostages were released on January 20,7987.
   Carter initially believed that his selec-
tion of negotiation lt'ould appeal to            po\\'er ... [and] to topplc from     tl'Le   posi-   payoff of -1 bv choosing ncgotiaiion and
Khomeini as well. 1'he president per-            tion of power anyone in any position                 apayoff of 3 by choosing military inter-
ceived that Khomeini faced serious               who is inclined to compromise with the               vention; if Khomeini chooses obstruc-
problems in Iran, such as demonstra-             East and West."                                      tion, Carter receives apayoff of 2by
tions by the unemployed and Iraqi in-               For Khomeini to have selected nego-               choosing negotiation and a payoff of 1
cursions across Iran's westem border. In         tiation would have rveakened his un-                 by choosing military intervention.
Carter's 1982 memoir, Keeping Fsith,he           compromising position. Iranian lead-                   Although Carter's dominant strategy
reported his belief that a U.S. choice of        ers who tried negotiating, including                 in both games is independent of
negotiation rvould give Khomeini a dig-          President Abolhassan Bani-Sadr and                   Khomeini's choice, Khomeini's best
nified way out of the impasse.                   Foreign Minister Sagdegh Ghotbzadeh,                 choice in the misperceived game de-
   The president also believed that              lost in the power struggle. Bani-Sadr                pends on what Carter selects. If Carter
Khomeini preferred a U.S. surrender              rvas forced to flee for his life to Paris,           chooses negotiation, which he should
that would result from the obshuction            and Ghotbzadeh was arrested and iat-                 because it is dominant Khomeini, an-
of negotiations. That result, Carter             er executed.                                         ticipating this, does better by choosing
thought, would give Khomeini his best               In the "real game"-the actual strate-             obstruction, which gives him a payoff
payolf of 4, whereas Khomeini would              gic situation-Khomeini most pre-                     of 4, rather than choosing negotiation,
get his next best payoff of 3 if both sides      ferred obstruction (4 and 3), regardless             r,vhich gives him a payoff of 3. So in the
selected negotiation. And finally, Carter        of the U.S. strategy choice. Doubtless,              misperceived game, Khomeini should
saw Khomeini getting inferior payoffs            he preferred that the United States                  choose obstruction, leading to the nego-
of 2 and 1 if the United States selected         choose negotiation (4) over military in-             tiation-obstruction outcome. That out-
military intervention.                           tervention (3).                                      come, which I call "Carter surrenders,"
                                                    \A/hat does classical game theory say             gives Carter a payoff of 2 and Khomeini
Carter's Miscalculations                         about the rational choices of the players            apayoff of 4.
Unfortunately for Carter, he misper-             in the misperceived game and the real                    Game theory calls this outcome-
ceived the strategic situation and, hence,       game? In both games, Carter's domi-                  Carter chooses negotiation and Khome-
played the wrong game. Khomeini                  nant, or unconditionally best, strategy              ini chooses obstruction-rational in the
wanted the total Islamization of Iranian         is negotiation. Regardless of what                   real game as well, because both players
society; he viewed the United States as          Khomeini chooses, Carter's payoff from               have dominant strategies associated
"a global Shah-a personification of              negotiation is better than his payoff                with it. In the real game, I call this out-
evil" that had to be cut off from any            from military intervention. Lr the mis-              come "Khomeini succeeds." (The other
contact with Iran. Khomeini abjured his          perceived game, for example, if Khome-               three outcomes in the real game are
nation never to "compromise with any             ini chooses negotiation, Carter gets            a    ranked differently by Khomeini from

                                                                                                              1993 November-December            569
those in the misperceived game, which        carrier USS Midlvay and its battle            there is cycling, it must be in a clock-
is why I give them different shorthand       group were already in the area. Those         wise direction.
descriptions.) In the real game, the ra-     two battle groups created the largest            If Carter believed that he had mov-
fionality of the (2, 4) outcome is rein-     U.S. naval force in the Indian Ocean          ing power-the ability to force Khome-
forced by Khomeini's dominant strate-        since World War II. But this vast array of    ini to stop in the move-countermove
$)'/of obstruction associated with it;       firepower proved useless, at least for the    process-Carter could force Khomeini
obstruction is not dominant in the real      purpose o{ inducing Khomeini to select        to stop at the negotiation-negotiation
game but, instead, Khomeini's best re-       negotiation.                                  outcome or the military interven-
sponse if Carter chooses his own domi-         The failed rescue operation in April        tion-obstruction outcome, which are
nant shategy of negotiation.                 1980 kept the situation at the negotia-       the two outcomes where Khomeini has
   Given that Carter does belter in both     tion-obstruction outcome for another          the next move. Khomeini would pre-
games by choosing negotiation, why           nine months. This was so despite the          fer the formet which gives him a pay-
would he consider, much less try, mili-      fact that Iranian leaders had concluded        off of 3, rather than the latter, which
tary intervention? Classical game theory     in August 1980-after the installation of      gives him a payoff of 1. In the real
does not give a reasory but the theory of    an Islamic govemment consistent with          game, however, these outcomes give
moves suggests the basis for his miscal-     Khomeini's theocratic vision-that             Khomeini payoffs of 2 and 3 respec-
culation. Carter might have thought-         keeping the hostages was a net liability.     tively, so he would choose to stay at the
with some justification in the misper-          Further complicating Iran's position       military intervention-obstruction out-
ceived game-that by threatening              was the attack by Iraqi forces in Sep-        come. As a consequence, Carter's
Khomeini with military intervention he       tember 1980. It was surely no accident        hoped-for negotiation-negotiation out-
would induce him to choose negotia-          that the hostages were set free on the        come in the misperceived game be-
tion, giving Carter the opportunity, by      day of Carter's departure from the            came, in April 1980, a military inter-
choosing negotiation himself, to obtain      \ /hite House on January 20,798L. Al'         vention-obstruction outcome in the
his best payoff.                             though Gary Sick claimsinOctober Sur-         real game.
   The reasoning underlying this calcu-      prise (1991) that the hostages were not          The theory of moves formally incor-
lation goes as follows: In the misper-       released before the November 1980             porates into the framework of game
ceived game, a negotiation-negotiation       presidential election because of a secret     theory an initial state in a payoff matrix,
outcome gives Carter his best payoff of      deal that Iran made with Ronald Rea-          possible moves and countermoves from
4 and gives Khomeini his next-best           gan's supporters, later congressional in-     it to try to reach a nonmyopic equilibri-
payoff of 3. A threat by Carter to           vestigations disputed Sick's claim, at        um, and threat and cycling to wear
choose military intervention, if carried     least regarding the involvement of            down an opponent. It also allows for
out, would inflict upon Khomeini his         George Bush.                                  the possibility that players possess only
two worst outcomes in the misper-               Perhaps Carter should not be judged        incomplete informatiory as I iliustrated
ceived game: a payoff of 2 if he chose       too harstrly for misperceiving the strate-    in the case of the Iran hostage crisis,
negotiation and a payoff of 1 if he          gic situation. If he had correctly foreseen   which can lead to misperception. As a
chose obstruction. Since Khomeini            the real game from the start, both game       theory that assumes that players can
would prefer a payoff of 2 over 1, he        theory and the theory of moves agree          rank outcomes but not necessarily at-
would choose negotiation, given              that he could not have moved away             tach utilities to them, it is eminently ap-
Carter's threat were credible. Howeveq,      from an outcome that gave him a payoff        plicable to the way we contemplate the
because both players do better by            of 2 and Khomeini apayoff of 4. What          strategic choices of others as we try to
choosing "compromis e" at (4, 3) rather      the theory of moves explains, and game        make our ownbest choices in a dy:ram-
than "Khomeini surrenders" at (3,2),         theory does not, is why Carter might          ic environment.
Khomeini should choose negotiation           have thought that he could implement
when Carter does, assuming that he           the compromise outcome through the            Bibliography
takes seriously Carter's threat of mili-     exercise of tfueats.                          Axelrod, Robert. 1984. The Ettolution of Coopera-
tary intervention.                              The theory of moves also shows how           flort. New York: Basic Books.
  There are two problems with this rea-      a series of moves and countermoves in         Brams, Steven J .7990. Negotiatiou Gantes: Apply-
soning. First, it is not clear that Carter   the misperceived game can induce this            hry Gnnre Tlrcory to Bargainirg and Arbitration.
                                                                                              New York: Routledge.
had what I call the "threat power"           outcome if Carter has what is called
                                             "moving power." Assume that ihe play-         Brams, Steven J. in press. Tlrcory of Mooes. Cam-
needed to induce a compromise out-
                                                                                              bridge, U.K.: Cambridge Unir.ersity Press.
come in the misperceived game. More          ers move and countermove in a clock-
                                                                                           Brams, Ster.en J., and Walter Mattli. 1993. Theo-
important, that was not the game being       wise direction on the misperceived-
                                                                                              ry of moves: overview and examples. Corr-
played. In the real game, Khomeini had       game payoff matrix. In that direction,          flict Mnnngenrcrft and Peace Science 12(2):7-39.
no reason to accede to a threat from         neither player ever moves from his best       Carter, Jimmy. 7982. Keeping Faith: Menroirs of n
Carter, because his political position       outcome (Carter vertically or Khomeini          President. New York: Baniam Books.
was stronger if he refused to compro-        horizontally). In a counterclockwise di-      Christopher, Warren (ed.). 1985. Anrcrican
mise. Regardless of Carter's choice,         rection, by contrast, players do move            Hoslages ilr lran: Tlrc Cottduct o/n Crisls.   New
                                                                                              Haven, CT: Yale University Press.
Khomeini does better by selecting ob-        from their best outcomes: Khomeini
                                                                                           Sick, Gary. 1991. October Sur1n'ise: Anrcricn's
struction in the real game.                  moves from a payoff of 4 at (2,4) when
                                                                                              Hostngas in lrnn ond tlrc Electiort of Ronald Rea-
   Nonetheless, Carter hied threats. He      he switches from obshuction to negoti-           gan. New York: Random House.
dispatched the aircraft carrier USS Kitfy    ation, and Carter moves from a payoff         Von Neumann, John, and Oskar Morgenstem.
Hawk and its supporting battle group         of 4 at (4,3) when he switches from ne-          1953. Tlwoty of Gantes nnd Econontic Behnuior.Srd
from the Pacific to the Arabian Sea. The     gotiation to military intervention. So, if       ed. Princeton, Nl]: Princeton University Press.

570    American Scientist, Volume   81

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