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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;" r '++ ? hri:* 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. Truels 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 qJ +J o (x,,Y,) ( x,,y.) prevents the selection of a common tar- L {{ r/) 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 (lJ +r (xr., y1) (xa,/r) theory of moves suggests a different \ ro +r outcome than does classical game theo- ry. In fact, the theory of moves provides b 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 u) 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- +J H t/l a) rc (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 {f) C/ F ro ! (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 (Play- 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 5. 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 _a .FJ government officials, Walter Mattli of ro _- E) 6i+ \e/ 4 the University of Chicago and I recon- structed the strategic thinking of deci- a) c ffi & & n ,. .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 L- {J> 7 'f&r bilities of the two opponents were al- -_ aJ =L E+- -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- ;ro _F, o ci't 2" 4 ondary goal was holding discussions with Iranian religious authorities about A) resolving the differences that had c strained relations between the United C 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. .:L ;AJ Carter considered two strategies: ne- IiJ 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