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ends. Each car is expected to keep the wheels on one side of the white line. As they approach each other, mutual destruction becomes more and more imminent. If one of them swerves from the white line before the other, the other, as they pass, shouts 'Chicken!', and the one who has swerved becomes an object of contempt. As played by irresponsible boys, this game is considered decadent and immoral, though only the lives of the players are risked. But when the game is played by eminent statesmen, who risk not only their own lives but those of many hundreds of millions of human beings, it is thought on both sides that the statesmen on one side are displaying a high degree of wisdom and courage, and only the statesmen on the other side are reprehensible. This, of course, is absurd. Both are to blame for playing such an incredibly dangerous game. The game may be played without misfortune a few times, but sooner or later, it will come to be felt that loss of face is more dreadful than nuclear annihilation. The moment will come when neither side can face the derisive cry of 'Chicken!' from the other side. When that moment comes, the statesmen of both sides will plunge the world into destruction.
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615:). The Nash equilibria are where the players' correspondences agree, i.e., cross. These are shown with points in the right hand graph. The best response mappings agree (i.e., cross) at three points. The first two Nash equilibria are in the top left and bottom right corners, where one player chooses one strategy, the other player chooses the opposite strategy. The third Nash equilibrium is a mixed strategy which lies along the diagonal from the bottom left to top right corners. If the players do not know which one of them is which, then the mixed Nash is an
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be seen as the evolution of a sort of prototypical version of ownership. Game-theoretically, however, there is nothing special about this solution. The opposite solution—where the owner plays dove and the intruder plays Hawk—is equally stable. In fact, this solution is present in a certain species of spider; when an invader appears the occupying spider leaves. In order to explain the prevalence of property rights over "anti-property rights" one must discover a way to break this additional symmetry.
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805:). In order for row players to choose one strategy and column players the other, the players must be able to distinguish which role (column or row player) they have. If no such uncorrelated asymmetry exists then both players must choose the same strategy, and the ESS will be the mixing Nash equilibrium. If there is an uncorrelated asymmetry, then the mixing Nash is not an ESS, but the two pure, role contingent, Nash equilibria are.
832:. In this model, a strategy which does better than the average increases in frequency at the expense of strategies that do worse than the average. There are two versions of the replicator dynamics. In one version, there is a single population which plays against itself. In another, there are two population models where each population only plays against the other population (and not against itself).
60:. The principle of the game is that while the ideal outcome is for one player to yield (to avoid the worst outcome if neither yields), individuals try to avoid it out of pride, not wanting to look like "chickens." Each player taunts the other to increase the risk of shame in yielding. However, when one player yields, the conflict is avoided, and the game essentially ends.
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polymorphic mixture of players dedicated to choosing a particular pure strategy(a single reaction differing from individual to individual). Biologically, these two options are strikingly different ideas. The Hawk–Dove game has been used as a basis for evolutionary simulations to explore which of these two modes of mixing ought to predominate in reality.
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presumed that the best thing for each driver is to stay straight while the other swerves (since the other is the "chicken" while a crash is avoided). Additionally, a crash is presumed to be the worst outcome for both players. This yields a situation where each player, in attempting to secure their best outcome, risks the worst.
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The single population model presents a situation where no uncorrelated asymmetries exist, and so the best players can do is randomize their strategies. The two population models provide such an asymmetry and the members of each population will then use that to correlate their strategies. In the two
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Because the loss of swerving is so trivial compared to the crash that occurs if nobody swerves, the reasonable strategy would seem to be to swerve before a crash is likely. Yet, knowing this, if one believes one's opponent to be reasonable, one may well decide not to swerve at all, in the belief that
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sought to deter
American attack by building a "doomsday machine", a device that would trigger world annihilation if Russia was hit by nuclear weapons or if any attempt were made to disarm it. However, the Russians had planned to signal the deployment of the machine a few days after having set it up,
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circles. The condition occurs when two or more areas of a product team claim they can deliver features at an unrealistically early date because each assumes the other teams are stretching the predictions even more than they are. This pretense continually moves forward past one project checkpoint to
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The standard biological interpretation of this uncorrelated asymmetry is that one player is the territory owner, while the other is an intruder on the territory. In most cases, the territory owner plays Hawk while the intruder plays Dove. In this sense, the evolution of strategies in Hawk–Dove can
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One tactic in the game is for one party to signal their intentions convincingly before the game begins. For example, if one party were to ostentatiously disable their steering wheel just before the match, the other party would be compelled to swerve. This shows that, in some circumstances, reducing
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for this game are presented here (Figures 1 and 2). In Figure 1, the outcomes are represented in words, where each player would prefer to win over tying, prefer to tie over losing, and prefer to lose over crashing. Figure 2 presents arbitrarily set numerical payoffs which theoretically conform to
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The practice of "schedule chicken" often results in contagious schedule slips due to the inter-team dependencies and is difficult to identify and resolve, as it is in the best interest of each team not to be the first bearer of bad news. The psychological drivers underlining the "schedule chicken"
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is another very influential model of aggression in biology. The two models investigate slightly different questions. The Hawk–Dove game is a model of escalation, and addresses the question of when ought an individual escalate to dangerously costly physical combat. The war of attrition seeks to
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Nash equilibrium, where both individuals randomly chose between playing Hawk/Straight or Dove/Swerve. This mixed strategy equilibrium is often sub-optimal—both players would do better if they could coordinate their actions in some way. This observation has been made independently in two different
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calls 'brinkmanship'. This is a policy adapted from a sport that, I am told, is practiced by some youthful degenerates. This sport is called 'Chicken!'. It is played by choosing a long, straight road with a white line down the middle and starting two very fast cars toward each other from opposite
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Like "Chicken", the "War of attrition" game models escalation of conflict, but they differ in the form in which the conflict can escalate. Chicken models a situation in which the catastrophic outcome differs in kind from the agreeable outcome, e.g., if the conflict is over life and death. War of
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The ESS for the Hawk–Dove game is a mixed strategy. Formal game theory is indifferent to whether this mixture is due to all players in a population choosing randomly between the two pure strategies (a range of possible instinctive reactions for a single situation) or whether the population is a
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for the Hawk–Dove game is given in Figure 3, where V is the value of the contested resource, and C is the cost of an escalated fight. It is (almost always) assumed that the value of the resource is less than the cost of a fight, i.e., C > V > 0. If C ≤ V, the
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The game of chicken models two drivers, both headed for a single-lane bridge from opposite directions. The first to swerve away yields the bridge to the other. If neither player swerves, the result is a costly deadlock in the middle of the bridge or a potentially fatal head-on collision. It is
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The hawk–dove version of the game imagines two players (animals) contesting an indivisible resource who can choose between two strategies, one more escalated than the other. They can use threat displays (play Dove), or physically attack each other (play Hawk). If both players choose the Hawk
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designed to avert the possibility of the opponent switching to aggressive behavior. The move involves a credible threat of the risk of irrational behavior in the face of aggression. If player 1 unilaterally moves to A, a rational player 2 cannot retaliate since (A, C) is preferable to
897:(A, A). Only if player 1 has grounds to believe that there is sufficient risk that player 2 responds irrationally (usually by giving up control over the response, so that there is sufficient risk that player 2 responds with A) player 1 will retract and agree on the compromise.
851:. (This occurs because the only ESS is the mixed strategy equilibrium.) In the two population model, this mixed point becomes unstable. In fact, the only stable states in the two population model correspond to the pure strategy equilibria, where one population is composed of all
159:, when first Bobby, and then later Lenny become stuck in their cars and drive off a cliff. The basic game-theoretic formulation of Chicken has no element of variable, potentially catastrophic, risk, and is also the contraction of a dynamic situation into a one-shot interaction.
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strategy, then they fight until one is injured and the other wins. If only one player chooses Hawk, then this player defeats the Dove player. If both players play Dove, there is a tie, and each player receives a payoff lower than the profit of a hawk defeating a dove.
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one's own options can be a good strategy. One real-world example is a protester who handcuffs themselves to an object, so that no threat can be made which would compel them to move (since they cannot move). Another example, taken from fiction, is found in
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in Figure 5 are the probabilities of playing the escalated strategy ("Hawk" or "Don't swerve") for players X and Y respectively. The line in graph on the left shows the optimum probability of playing the escalated strategy for player Y as a function of
63:
The name "chicken" has its origins in a game in which two drivers drive toward each other on a collision course: one must swerve, or both may die in the crash, but if one driver swerves and the other does not, the one who swerved will be called a
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Brinkmanship involves the introduction of an element of uncontrollable risk: even if all players act rationally in the face of risk, uncontrollable events can still trigger the catastrophic outcome. In the "chickie run" scene from the film
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attrition models a situation in which the outcomes differ only in degrees, such as a boxing match in which the contestants have to decide whether the ultimate prize of victory is worth the ongoing cost of deteriorating health and stamina.
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The exact value of the Dove vs. Dove payoff varies between model formulations. Sometimes the players are assumed to split the payoff equally (V/2 each), other times the payoff is assumed to be zero (since this is the expected payoff to a
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population model, one population gains at the expense of another. Hawk–Dove and
Chicken thus illustrate an interesting case where the qualitative results for the two different versions of the replicator dynamics differ wildly.
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While the Hawk–Dove game is typically taught and discussed with the payoffs in terms of V and C, the solutions hold true for any matrix with the payoffs in Figure 4, where W > T > L > X.
76:. The name "hawk–dove" refers to a situation in which there is a competition for a shared resource and the contestants can choose either conciliation or conflict; this terminology is most commonly used in
497:, and differences in the value of winning to the different players, allowing the players to threaten each other before choosing moves in the game, and extending the interaction to two plays of the game.
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if the threat is one of two possible signals ("I will not swerve" or "I will swerve"), or they will be costless if there are three or more signals (in which case the signals will function as a game of "
754:). This exogenous draw event is assumed to be uniformly at random over the 3 outcomes. After drawing the card the third party informs the players of the strategy assigned to them on the card (but
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pictured in Figure 7a. The one-dimensional vector field of the single population model (Figure 7b) corresponds to the bottom left to top right diagonal of the two population model.
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playing different strategies. The underlying concept is that players use a shared resource. In coordination games, sharing the resource creates a benefit for all: the resource is
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of the game. Notably, the expected payoff for this equilibrium is 7(1/3) + 2(1/3) + 6(1/3) = 5 which is higher than the expected payoff of the mixed strategy Nash equilibrium.
465:
Hawk–Dove transforming into
Prisoner's Dilemma. As C becomes smaller than V, the mixed strategy equilibrium moves to the pure strategy equilibrium of both players playing hawk
931:. Both players accrue costs while displaying at each other, the contest ends when the individual making the lower bid quits. Both players will then have paid the lower bid.
762:, they would not want to deviate supposing the other player played their assigned strategy since they will get 7 (the highest payoff possible). Suppose a player is assigned
619:(ESS), as play is confined to the bottom left to top right diagonal line. Otherwise an uncorrelated asymmetry is said to exist, and the corner Nash equilibria are ESSes.
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the opponent will be reasonable and decide to swerve, leaving the first player the winner. This unstable situation can be formalized by saying there is more than one
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Biologists have explored modified versions of classic Hawk–Dove game to investigate a number of biologically relevant factors. These include adding variation in
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emptation payoff, should the other player use the less escalated move). The essential difference between these two games is that in the prisoner's dilemma, the
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contingent strategy profiles, in which each player plays one of the pair of strategies, and the other player chooses the opposite strategy. The third one is a
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where Ren McCormack is stuck in his tractor and hence wins the game as they cannot play "chicken". A similar event happens in two different games in the film
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is also used as a metaphor for a situation where two parties engage in a showdown where they have nothing to gain and only pride stops them from backing down.
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strategy is dominated, whereas in
Chicken the equivalent move is not dominated since the outcome payoffs when the opponent plays the more escalated move (
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of Daring is 0(1/2) + 7(1/2) = 3.5 and the expected utility of chickening out is 2(1/2) + 6(1/2) = 4. So, the player would prefer to chicken out.
959:. PD is about the impossibility of cooperation while Chicken is about the inevitability of conflict. Iterated play can solve PD but not Chicken.
321:, which is a pair of strategies for which neither player gains by changing their own strategy while the other stays the same. (In this case, the
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Players may also make non-binding threats to not swerve. This has been modeled explicitly in the Hawk–Dove game. Such threats work, but must be
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Since neither player has an incentive to deviate from the drawn assignments, this probability distribution over the strategies is known as a
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In the one population model, the only stable state is the mixed strategy Nash equilibrium. Every initial population proportion (except all
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293:, in which it is mutually beneficial for the players to play different strategies. In this way, it can be thought of as the opposite of a
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927:(an all-pay second price auction). The bids are assumed to be the duration which the player is willing to persist in making a costly
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s. In this model one population becomes the aggressive population while the other becomes passive. This model is illustrated by the
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answer the question of how contests may be resolved when there is no possibility of physical combat. The war of attrition is an
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595:. The line in the second graph shows the optimum probability of playing the escalated strategy for player X as a function of
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892:" are often used synonymously in the context of conflict, but in the strict game-theoretic sense, "brinkmanship" refers to a
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84:. From a game-theoretic point of view, "chicken" and "hawk–dove" are identical. The game has also been used to describe the
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Fig.5 - Reaction correspondences for both players in a discoordination game. Compare with replicator dynamic vector fields
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equilibrium where each player Dares with probability 1/3. It results in expected payoffs of 14/3 = 4.667 for each player.
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this situation. Here, the benefit of winning is 1, the cost of losing is -1, and the cost of crashing is -1000.
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The Hawk–Dove game is the most commonly used game theoretical model of aggressive interactions in biology. The
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Since the nuclear stalemate became apparent, the governments of East and West have adopted the policy that
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Consider the version of "Chicken" pictured in Figure 6. Like all forms of the game, there are three
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441:, this game is known as Hawk–Dove. The earliest presentation of a form of the Hawk–Dove game was by
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Chicken is a symmetrical 2x2 game with conflicting interests, the preferred outcome is to play
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Although there are three Nash equilibria in the Hawk–Dove game, the one which emerges as the
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chooses between the two pure strategies. Either the pure, or mixed, Nash equilibria will be
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Now consider a third party (or some natural event) that draws one of three cards labeled: (
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payoff C (see tables below). The temptation away from this sensible outcome is toward a
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equilibria are the two situations wherein one player swerves while the other does not.)
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1553:(1998). "On the evolution of behavioral heterogeneity in individuals and populations".
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843:) converge to the mixed strategy Nash Equilibrium where part of the population plays
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A formal version of the game of
Chicken has been the subject of serious research in
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is a symmetrical 2x2 game with conflicting interests: the preferred outcome is to
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mapping for all 2x2 anti-coordination games is shown in Figure 5. The variables
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game, which is the presumed models for a contest decided by display duration).
17:
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Game Theory Topics: Incomplete
Information, Repeated Games, and N-Player Games
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Maynard Smith, John; Parker, Geoff A. (1973). "The Logic of Animal
Conflict".
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which, because of an unfortunate course of events, turned out to be too late.
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Fig 7a: Vector field for two population replicator dynamics and Hawk–Dove
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the strategy assigned to their opponent). Suppose a player is assigned
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with probability 1/2 (due to the nature of the exogenous draw). The
1171:, a naval tactic of intentional suicidal ramming into an enemy ship
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1904:
The
Mediation Process: Practical Strategies for Resolving Conflict
1614:
The
Resolution of Conflict: Constructive and Destructive Processes
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539:
460:
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in their paper, "The logic of animal conflict". The traditional
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1735:
Kim, Y-G. (1995). "Status signaling games in animal contests".
1495:
The
Patterns Handbook: Techniques, Strategies, and Applications
870:
Fig. 7b: Vector field for single population replicator dynamics
1449:"Punishment in Iterated Chicken and Prisoner's Dilemma Games"
37:"Snow-drift" redirects here. For the natural phenomenon, see
789:
Uncorrelated asymmetries and solutions to the hawk–dove game
309:. In anti-coordination games the resource is rivalrous but
68:", meaning a coward; this terminology is most prevalent in
1141:
begins or just before the functionality is actually due.
1029:
in the prisoner's dilemma, such that players receive the
454:
resulting game is not a game of Chicken but is instead a
313:
and sharing comes at a cost (or negative externality).
1584:"Evolutionary Stability for Two-stage Hawk-Dove Games"
1430:
1998. Evolutionary Genetics. Oxford University Press.
998:
Prisoner's dilemma. Payoff ranks (to Row player) are:
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is a simple model of strategy change commonly used in
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Chicken/Hawk–Dove. Payoff ranks (to Row player) are:
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The game of Chicken as a metaphor for human conflict
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3001:
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2727:
2509:
2411:
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2176:
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1338:. Cambridge New York: Cambridge University Press.
1388:Kahn (1965), cited in Rapoport and Chammah (1966)
1231:
1278:Rapoport and Chammah (1966) pp. 10–14 and 23–28.
1242:
1240:
27:Model of conflict for two players in game theory
1925:; Chammah, A.M. (1966). "The Game of Chicken".
1041:move in the prisoner's dilemma (generating the
623:Strategy polymorphism vis-à-vis strategy mixing
652:Correlated equilibrium and the game of chicken
2052:
1497:, page 169. Cambridge University Press, 1998.
1405:
1403:
1263:
1261:
1145:behavior in many ways mimic the hawk–dove or
8:
1826:(1976). "The logic of asymmetric contests".
1685:"The Role of Asymmetries in Animal Contests"
636:In both "Chicken" and "Hawk–Dove", the only
56:, is a model of conflict for two players in
1660:Fink, E.C.; Gates, S.; Humes, B.D. (1998).
766:. Then the other player has been assigned
2059:
2045:
2037:
1601:
648:contexts, with almost identical results.
536:Best response mapping and Nash equilibria
120:famously compared the game of Chicken to
1980:. New York: Cambridge University Press.
1862:(1973). "The logic of animal conflict".
797:(ESS) depends upon the existence of any
599:(the axes have not been rotated, so the
545:
468:
305:, and the shared usage creates positive
2031:Game of Chicken – Rebel Without a Cause
1329:
1327:
1221:
1120:Schedule chicken and project management
551:All anti-coordination games have three
1718:On escalation: metaphors and scenarios
1255:Dixit and Nalebuff (1991) pp. 205–222.
1589:Rocky Mountain Journal of Mathematics
1366:
1364:
7:
1617:. Yale University Press, New Haven.
1227:
1225:
923:in which both players pay the lower
1510:, page 33. Safari Tech Books, 2000.
1397:Bergstrom and Goddfrey-Smith (1998)
2108:First-player and second-player win
2026:Game-theoretic analysis of Chicken
1958:. George Allen and Unwin, London.
563:equilibrium, in which each player
297:, where playing the same strategy
25:
1801:Evolution and the Theory of Games
1447:Jankowski, Richard (1990-10-01).
1336:Evolution and the theory of games
1268:Maynard Smith & Parker (1976)
847:and part of the population plays
2215:Coalition-proof Nash equilibrium
1978:Evolution of the Social Contract
1956:Common Sense and Nuclear Warfare
569:evolutionarily stable strategies
1720:. Praeger Publ. Co., New York.
1232:Osborne & Rubinstein (1994)
289:Both Chicken and Hawk–Dove are
267:Fig. 2: Chicken with numerical
2225:Evolutionarily stable strategy
1907:. Jossey-Bass, San Francisco.
1901:Moore, Christopher W. (1986).
1804:. Cambridge University Press.
1737:Journal of Theoretical Biology
935:Chicken and prisoner's dilemma
910:Hawk–dove and war of attrition
795:evolutionarily stable strategy
617:evolutionarily stable strategy
424:Fig. 4: General Hawk–Dove game
1:
2153:Simultaneous action selection
1927:American Behavioral Scientist
1840:10.1016/S0003-3472(76)80110-8
1701:10.1016/S0003-3472(81)80166-2
801:in the game (in the sense of
3085:List of games in game theory
2265:Quantal response equilibrium
2255:Perfect Bayesian equilibrium
2190:Bayes correlated equilibrium
1999:. Cambridge, MA: MIT Press.
1522:"Macronomics: February 2012"
1508:Planning Extreme Programming
1334:Maynard Smith, John (1982).
879:Related strategies and games
692:Fig. 6: A version of Chicken
2554:Optional prisoner's dilemma
2285:Self-confirming equilibrium
1995:Weibull, Jörgen W. (1995).
1465:10.1177/1043463190002004004
1418:Weibull (1995) pp. 183–184.
466:
167:Game theoretic applications
3152:
3136:Social science experiments
3019:Principal variation search
2735:Aumann's agreement theorem
2398:Strategy-stealing argument
2310:Trembling hand equilibrium
2240:Markov perfect equilibrium
2235:Mertens-stable equilibrium
1939:10.1177/000276426601000303
495:resource holding potential
469:§ Replicator dynamics
430:
86:mutual assured destruction
36:
29:
3055:Combinatorial game theory
2714:Princess and monster game
2270:Quasi-perfect equilibrium
2195:Bayesian Nash equilibrium
1195:Si vis pacem, para bellum
1094:
1025:in the Chicken game, and
996:
955:while the opponent plays
943:while the opponent plays
770:with probability 1/2 and
690:
439:the biological literature
422:
379:
265:
218:
92:, especially the sort of
3126:Evolutionary game theory
3070:Evolutionary game theory
2803:Antoine Augustin Cournot
2689:Guess 2/3 of the average
2486:Strictly determined game
2280:Satisfaction equilibrium
2098:Escalation of commitment
1997:Evolutionary Game Theory
1683:Hammerstein, P. (1981).
1611:Deutsch, Morton (1974).
1409:Skyrms (1996) pp. 76–79.
830:evolutionary game theory
573:uncorrelated asymmetries
433:Evolutionary game theory
82:evolutionary game theory
32:Chicken (disambiguation)
3075:Glossary of game theory
2674:Stackelberg competition
2300:Strong Nash equilibrium
1778:A course in game theory
1603:10.1216/rmjm/1181072273
1567:10.1023/A:1006588918909
1524:. Macronomy.blogspot.in
1506:Beck, K and Fowler, M:
1453:Rationality and Society
1137:the next until feature
934:
803:anti-coordination games
571:depending upon whether
291:anti-coordination games
281:. Two versions of the
3100:Tragedy of the commons
3080:List of game theorists
3060:Confrontation analysis
2770:Sprague–Grundy theorem
2290:Sequential equilibrium
2210:Correlated equilibrium
1954:Russell, B.W. (1959).
1757:10.1006/jtbi.1995.0193
1642:Thinking Strategically
1555:Biology and Philosophy
1037:move in Chicken and a
871:
822:
799:uncorrelated asymmetry
783:correlated equilibrium
548:
473:
381:Fig. 3: Hawk–Dove game
138:
3121:Non-cooperative games
2873:Jean-François Mertens
1582:Cressman, R. (1995).
1246:Russell (1959) p. 30.
1190:Ritualized aggression
869:
855:and the other of all
820:
707:Nash equilibria are (
543:
530:rock, paper, scissors
464:
144:Rebel Without a Cause
129:
3002:Search optimizations
2878:Jennifer Tour Chayes
2765:Revelation principle
2760:Purification theorem
2699:Nash bargaining game
2664:Bertrand competition
2649:El Farol Bar problem
2614:Electronic mail game
2579:Lewis signaling game
2123:Hierarchy of beliefs
1772:Osborne, Martin J.;
1551:Godfrey-Smith, Peter
1134:software development
723:). There is also a
609:independent variable
555:. Two of these are
516:. In that film, the
98:Cuban Missile Crisis
48:, also known as the
30:For other uses, see
3050:Bounded rationality
2669:Cournot competition
2619:Rock paper scissors
2594:Battle of the sexes
2584:Volunteer's dilemma
2456:Perfect information
2383:Dominant strategies
2220:Epsilon-equilibrium
2103:Extensive-form game
1878:1973Natur.246...15S
1856:Maynard Smith, John
1820:Maynard Smith, John
1796:Maynard Smith, John
1749:1995JThBi.176..221K
1358:Hammerstein (1981).
1302:1973Natur.246...15S
1200:Volunteer's dilemma
1027:Cooperate-Cooperate
826:Replicator dynamics
813:Replicator dynamics
3029:Paranoid algorithm
3009:Alpha–beta pruning
2888:John Maynard Smith
2719:Rendezvous problem
2559:Traveler's dilemma
2549:Gift-exchange game
2544:Prisoner's dilemma
2461:Large Poisson game
2428:Bargaining problem
2333:Backward induction
2305:Subgame perfection
2260:Proper equilibrium
2033:by Elmer G. Wiens.
1637:Nalebuff, Barry J.
1547:Bergstrom, Carl T.
1185:Prisoner's dilemma
1130:project management
949:prisoner's dilemma
947:. Similarly, the
872:
823:
611:is plotted on the
603:is plotted on the
601:dependent variable
549:
489:Hawk–dove variants
474:
456:Prisoner's Dilemma
443:John Maynard Smith
261:-1000, -1000
3108:
3107:
3014:Aspiration window
2983:Suzanne Scotchmer
2938:Oskar Morgenstern
2833:Donald B. Gillies
2775:Zermelo's theorem
2704:Induction puzzles
2659:Fair cake-cutting
2634:Public goods game
2564:Coordination game
2438:Intransitive game
2368:Forward induction
2250:Pareto efficiency
2230:Gibbs equilibrium
2200:Berge equilibrium
2148:Simultaneous game
1914:978-0-87589-673-1
1811:978-0-521-28884-2
1774:Rubinstein, Ariel
1727:978-0-313-25163-4
1716:Kahn, H. (1965).
1633:Dixit, Avinash K.
1624:978-0-300-01683-3
1436:978-0-19-850231-9
1428:Maynard Smith, J.
1345:978-0-521-28884-2
1164:Coordination game
1117:
1116:
1104:oordination >
1019:
1018:
1006:oordination >
697:
696:
632:Symmetry breaking
565:probabilistically
526:wastefully costly
429:
428:
386:
385:
375:
368:
358:
353:
295:coordination game
275:
274:
229:
228:
214:
213:Crash, Crash
209:
199:
194:
70:political science
16:(Redirected from
3143:
3095:Topological game
3090:No-win situation
2988:Thomas Schelling
2968:Robert B. Wilson
2928:Merrill M. Flood
2898:John von Neumann
2808:Ariel Rubinstein
2793:Albert W. Tucker
2644:War of attrition
2604:Matching pennies
2245:Nash equilibrium
2168:Mechanism design
2133:Normal-form game
2088:Cooperative game
2061:
2054:
2047:
2038:
2010:
1991:
1969:
1950:
1923:Rapoport, Anatol
1918:
1897:
1886:10.1038/246015a0
1860:Price, George R.
1851:
1828:Animal Behaviour
1824:Parker, Geoff A.
1815:
1791:
1768:
1731:
1712:
1689:Animal Behaviour
1679:
1667:
1656:
1628:
1607:
1605:
1578:
1533:
1532:
1530:
1529:
1517:
1511:
1504:
1498:
1491:
1485:
1484:
1444:
1438:
1425:
1419:
1416:
1410:
1407:
1398:
1395:
1389:
1386:
1380:
1379:Cressman (1995).
1377:
1371:
1368:
1359:
1356:
1350:
1349:
1331:
1322:
1321:
1310:10.1038/246015a0
1285:
1279:
1276:
1270:
1265:
1256:
1253:
1247:
1244:
1235:
1229:
1205:War of attrition
1180:Mexican standoff
1175:Matching pennies
1126:schedule chicken
1060:
1057:) are reversed.
962:
916:war of attrition
901:War of attrition
776:expected utility
656:
641:Nash equilibrium
479:war of attrition
472:
388:
374:
371:
366:
356:
352:
351:(V−C)/2, (V−C)/2
349:
333:
319:Nash equilibrium
299:Pareto dominates
231:
212:
207:
197:
192:
176:
156:The Heavenly Kid
118:Bertrand Russell
104:Popular versions
96:involved in the
21:
3151:
3150:
3146:
3145:
3144:
3142:
3141:
3140:
3131:Endurance games
3111:
3110:
3109:
3104:
3038:
3024:max^n algorithm
2997:
2993:William Vickrey
2953:Reinhard Selten
2908:Kenneth Binmore
2823:David K. Levine
2818:Daniel Kahneman
2785:
2779:
2755:Negamax theorem
2745:Minimax theorem
2723:
2684:Diner's dilemma
2539:All-pay auction
2505:
2491:Stochastic game
2443:Mean-field game
2414:
2407:
2378:Markov strategy
2314:
2180:
2172:
2143:Sequential game
2128:Information set
2113:Game complexity
2083:Congestion game
2071:
2065:
2017:
2007:
1994:
1988:
1972:
1966:
1953:
1921:
1915:
1900:
1872:(5427): 15–18.
1854:
1818:
1812:
1794:
1788:
1771:
1734:
1728:
1715:
1682:
1676:
1659:
1653:
1645:. W.W. Norton.
1631:
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1542:
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1408:
1401:
1396:
1392:
1387:
1383:
1378:
1374:
1369:
1362:
1357:
1353:
1346:
1333:
1332:
1325:
1296:(5427): 15–18.
1287:
1286:
1282:
1277:
1273:
1266:
1259:
1254:
1250:
1245:
1238:
1230:
1223:
1218:
1155:
1147:snowdrift model
1122:
1100:emptation >
1002:emptation >
937:
912:
903:
888:"Chicken" and "
886:
881:
815:
791:
701:Nash equilibria
654:
634:
625:
553:Nash equilibria
538:
513:Dr. Strangelove
508:Stanley Kubrick
503:
491:
435:
372:
350:
331:
174:
169:
114:game of chicken
106:
90:nuclear warfare
46:game of chicken
42:
35:
28:
23:
22:
18:Game of chicken
15:
12:
11:
5:
3149:
3147:
3139:
3138:
3133:
3128:
3123:
3113:
3112:
3106:
3105:
3103:
3102:
3097:
3092:
3087:
3082:
3077:
3072:
3067:
3062:
3057:
3052:
3046:
3044:
3040:
3039:
3037:
3036:
3031:
3026:
3021:
3016:
3011:
3005:
3003:
2999:
2998:
2996:
2995:
2990:
2985:
2980:
2975:
2970:
2965:
2960:
2958:Robert Axelrod
2955:
2950:
2945:
2940:
2935:
2933:Olga Bondareva
2930:
2925:
2923:Melvin Dresher
2920:
2915:
2913:Leonid Hurwicz
2910:
2905:
2900:
2895:
2890:
2885:
2880:
2875:
2870:
2865:
2860:
2855:
2850:
2848:Harold W. Kuhn
2845:
2840:
2838:Drew Fudenberg
2835:
2830:
2828:David M. Kreps
2825:
2820:
2815:
2813:Claude Shannon
2810:
2805:
2800:
2795:
2789:
2787:
2781:
2780:
2778:
2777:
2772:
2767:
2762:
2757:
2752:
2750:Nash's theorem
2747:
2742:
2737:
2731:
2729:
2725:
2724:
2722:
2721:
2716:
2711:
2706:
2701:
2696:
2691:
2686:
2681:
2676:
2671:
2666:
2661:
2656:
2651:
2646:
2641:
2636:
2631:
2626:
2621:
2616:
2611:
2609:Ultimatum game
2606:
2601:
2596:
2591:
2589:Dollar auction
2586:
2581:
2576:
2574:Centipede game
2571:
2566:
2561:
2556:
2551:
2546:
2541:
2536:
2531:
2529:Infinite chess
2526:
2521:
2515:
2513:
2507:
2506:
2504:
2503:
2498:
2496:Symmetric game
2493:
2488:
2483:
2481:Signaling game
2478:
2476:Screening game
2473:
2468:
2466:Potential game
2463:
2458:
2453:
2445:
2440:
2435:
2430:
2425:
2419:
2417:
2409:
2408:
2406:
2405:
2400:
2395:
2393:Mixed strategy
2390:
2385:
2380:
2375:
2370:
2365:
2360:
2355:
2350:
2345:
2340:
2335:
2330:
2324:
2322:
2316:
2315:
2313:
2312:
2307:
2302:
2297:
2292:
2287:
2282:
2277:
2275:Risk dominance
2272:
2267:
2262:
2257:
2252:
2247:
2242:
2237:
2232:
2227:
2222:
2217:
2212:
2207:
2202:
2197:
2192:
2186:
2184:
2174:
2173:
2171:
2170:
2165:
2160:
2155:
2150:
2145:
2140:
2135:
2130:
2125:
2120:
2118:Graphical game
2115:
2110:
2105:
2100:
2095:
2090:
2085:
2079:
2077:
2073:
2072:
2066:
2064:
2063:
2056:
2049:
2041:
2035:
2034:
2028:
2023:
2016:
2015:External links
2013:
2012:
2011:
2005:
1992:
1986:
1970:
1964:
1951:
1919:
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1898:
1852:
1816:
1810:
1792:
1786:
1769:
1743:(2): 221–231.
1732:
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1674:
1657:
1651:
1629:
1623:
1608:
1579:
1561:(2): 205–231.
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1459:(4): 449–470.
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929:threat display
911:
908:
902:
899:
894:strategic move
885:
882:
880:
877:
814:
811:
790:
787:
725:mixed strategy
695:
694:
688:
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666:
665:
662:
659:
653:
650:
645:mixed strategy
633:
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621:
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501:Pre-commitment
499:
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431:Main article:
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198:Lose, Win
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54:snowdrift game
50:hawk-dove game
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3043:Miscellaneous
3041:
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3015:
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3010:
3007:
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3004:
3000:
2994:
2991:
2989:
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2984:
2981:
2979:
2978:Samuel Bowles
2976:
2974:
2973:Roger Myerson
2971:
2969:
2966:
2964:
2963:Robert Aumann
2961:
2959:
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2946:
2944:
2941:
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2936:
2934:
2931:
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2926:
2924:
2921:
2919:
2918:Lloyd Shapley
2916:
2914:
2911:
2909:
2906:
2904:
2903:Kenneth Arrow
2901:
2899:
2896:
2894:
2891:
2889:
2886:
2884:
2883:John Harsanyi
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2859:
2856:
2854:
2853:Herbert Simon
2851:
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2657:
2655:
2654:Fair division
2652:
2650:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2630:
2629:Dictator game
2627:
2625:
2622:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2597:
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2522:
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2517:
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2514:
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2508:
2502:
2501:Zero-sum game
2499:
2497:
2494:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2474:
2472:
2471:Repeated game
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2389:
2388:Pure strategy
2386:
2384:
2381:
2379:
2376:
2374:
2371:
2369:
2366:
2364:
2361:
2359:
2356:
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2353:De-escalation
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2295:Shapley value
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2201:
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2191:
2188:
2187:
2185:
2183:
2179:
2175:
2169:
2166:
2164:
2163:Succinct game
2161:
2159:
2156:
2154:
2151:
2149:
2146:
2144:
2141:
2139:
2136:
2134:
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2019:
2018:
2014:
2008:
2006:0-262-23181-6
2002:
1998:
1993:
1989:
1987:0-521-55583-3
1983:
1979:
1975:
1974:Skyrms, Brian
1971:
1967:
1965:0-04-172003-2
1961:
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1787:0-262-65040-1
1783:
1780:. MIT press.
1779:
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1149:of conflict.
1148:
1142:
1140:
1135:
1131:
1128:" is used in
1127:
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1103:
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1024:
1023:Swerve-Swerve
1015:
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705:pure strategy
702:
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580:best response
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451:payoff matrix
448:
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335:
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328:
326:
324:
323:pure strategy
320:
314:
312:
308:
307:externalities
304:
303:non-rivalrous
300:
296:
292:
287:
284:
283:payoff matrix
280:
271:
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260:
257:
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242:
238:
235:
233:
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222:payoff matrix
217:
211:
206:
203:
202:
196:
193:Tie, Tie
191:
188:
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171:
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61:
59:
55:
51:
47:
40:
33:
19:
2948:Peyton Young
2943:Paul Milgrom
2858:Hervé Moulin
2798:Amos Tversky
2740:Folk theorem
2568:
2451:-player game
2448:
2373:Grim trigger
1996:
1977:
1955:
1933:(3): 10–28.
1930:
1926:
1903:
1869:
1863:
1831:
1827:
1800:
1777:
1740:
1736:
1717:
1692:
1688:
1663:
1641:
1613:
1593:
1587:
1558:
1554:
1526:. Retrieved
1515:
1507:
1502:
1494:
1489:
1456:
1452:
1442:
1423:
1414:
1393:
1384:
1375:
1354:
1335:
1293:
1289:
1283:
1274:
1251:
1234:, p. 30
1159:Brinkmanship
1143:
1123:
1109:
1108:eutral >
1105:
1101:
1097:
1095:
1054:
1053:in place of
1050:
1046:
1042:
1038:
1034:
1031:Coordination
1030:
1026:
1022:
1020:
1011:
1010:eutral >
1007:
1003:
999:
997:
956:
952:
944:
940:
938:
913:
904:
890:Brinkmanship
887:
884:Brinkmanship
873:
861:vector field
856:
852:
848:
844:
840:
836:
834:
824:
807:
792:
780:
771:
767:
763:
759:
755:
751:
747:
743:
739:
735:
731:
729:
720:
716:
712:
708:
698:
691:
635:
626:
596:
592:
587:
583:
577:
550:
523:
511:
504:
492:
483:
475:
447:George Price
436:
423:
380:
315:
290:
288:
276:
266:
258:+1, -1
250:-1, +1
219:
161:
154:
148:
142:
139:
130:
125:brinkmanship
113:
111:
107:
94:brinkmanship
62:
53:
49:
45:
43:
3065:Coopetition
2868:Jean Tirole
2863:John Conway
2843:Eric Maskin
2639:Blotto game
2624:Pirate game
2433:Global game
2403:Tit for tat
2338:Bid shading
2328:Appeasement
2178:Equilibrium
2158:Solved game
2093:Determinacy
2076:Definitions
2069:game theory
1834:: 159–175.
1695:: 193–205.
1596:: 145–155.
1493:Rising, L:
1370:Kim (1995).
1139:integration
703:. The two
279:game theory
112:The phrase
58:game theory
3115:Categories
2709:Trust game
2694:Kuhn poker
2363:Escalation
2358:Deterrence
2348:Cheap talk
2320:Strategies
2138:Preference
2067:Topics of
1540:References
1528:2012-08-13
1520:Martin T.
1124:The term "
1112:unishment.
1014:unishment.
986:Cooperate
970:Cooperate
607:, and the
247:0, 0
224:of Chicken
220:Fig. 1: A
133:Mr. Dulles
2893:John Nash
2599:Stag hunt
2343:Collusion
1947:144436238
1481:144109323
1473:1043-4631
1073:Straight
1065:Straight
1047:Cooperate
957:Cooperate
638:symmetric
329:Hawk–dove
255:Straight
239:Straight
204:Straight
184:Straight
150:Footloose
74:economics
39:Snowdrift
3034:Lazy SMP
2728:Theorems
2679:Deadlock
2534:Checkers
2415:of games
2182:concepts
1976:(1996).
1848:53161069
1798:(1982).
1776:(1994).
1709:53196318
1668:. Sage.
1639:(1991).
1575:27501303
1210:Zugzwang
1169:Fireship
1153:See also
1051:Straight
1035:Straight
941:Straight
839:and all
746:), and (
680:Chicken
664:Chicken
613:ordinate
605:abscissa
518:Russians
373:V/2, V/2
2786:figures
2569:Chicken
2423:Auction
2413:Classes
1894:4224989
1874:Bibcode
1765:7475112
1745:Bibcode
1318:4224989
1298:Bibcode
1084:Swerve
1068:Swerve
975:Defect
967:Defect
921:auction
715:) and (
643:is the
575:exist.
269:payoffs
244:Swerve
236:Swerve
189:Swerve
181:Swerve
172:Chicken
122:nuclear
78:biology
66:chicken
2003:
1984:
1962:
1945:
1911:
1892:
1865:Nature
1846:
1808:
1784:
1763:
1724:
1707:
1672:
1649:
1621:
1573:
1479:
1471:
1434:
1342:
1316:
1290:Nature
1055:Defect
1039:Defect
953:Defect
945:Swerve
2524:Chess
2511:Games
1943:S2CID
1890:S2CID
1844:S2CID
1705:S2CID
1571:S2CID
1477:S2CID
1314:S2CID
1216:Notes
853:Hawks
669:Dare
661:Dare
561:mixed
546:below
467:(see
418:T, T
415:L, W
412:Dove
407:W, L
404:X, X
401:Hawk
396:Dove
393:Hawk
363:Dove
346:Hawk
341:Dove
338:Hawk
2205:Core
2001:ISBN
1982:ISBN
1960:ISBN
1909:ISBN
1806:ISBN
1782:ISBN
1761:PMID
1722:ISBN
1670:ISBN
1647:ISBN
1619:ISBN
1469:ISSN
1432:ISBN
1340:ISBN
1132:and
857:Dove
849:Dove
845:Hawk
841:Dove
837:Hawk
738:), (
686:6,6
683:2,7
675:7,2
672:0,0
586:and
578:The
557:pure
532:").
445:and
367:0, V
357:V, 0
80:and
72:and
44:The
2784:Key
1935:doi
1882:doi
1870:246
1836:doi
1753:doi
1741:176
1697:doi
1598:doi
1563:doi
1461:doi
1306:doi
1294:246
925:bid
756:not
510:'s
437:In
88:of
52:or
3117::
2519:Go
1941:.
1931:10
1929:.
1888:.
1880:.
1868:.
1858:;
1842:.
1832:24
1830:.
1822:;
1759:.
1751:.
1739:.
1703:.
1693:29
1691:.
1687:.
1635:;
1594:25
1592:.
1586:.
1569:.
1559:13
1557:.
1549:;
1475:.
1467:.
1455:.
1451:.
1402:^
1363:^
1326:^
1312:.
1304:.
1292:.
1260:^
1239:^
1224:^
1090:C
1087:N
1079:T
1076:P
992:C
989:P
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978:N
750:,
742:,
734:,
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711:,
471:).
458:.
100:.
2449:n
2060:e
2053:t
2046:v
2009:.
1990:.
1968:.
1949:.
1937::
1917:.
1896:.
1884::
1876::
1850:.
1838::
1814:.
1790:.
1767:.
1755::
1747::
1730:.
1711:.
1699::
1678:.
1655:.
1627:.
1606:.
1600::
1577:.
1565::
1531:.
1483:.
1463::
1457:2
1348:.
1320:.
1308::
1300::
1110:P
1106:N
1102:C
1098:T
1043:T
1012:P
1008:N
1004:C
1000:T
772:D
768:C
764:C
760:D
752:D
748:C
744:C
740:D
736:C
732:C
721:D
717:C
713:C
709:D
597:y
593:x
588:y
584:x
127::
64:"
41:.
34:.
20:)
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