The game of Chicken, also known as the Hawk-Dove game, is an influential model of conflict for two players in game theory. The principle of the game is that while each player prefers not to yield to the other, the outcome where neither player yields is the worst possible one for both players. The name "Chicken" has its origins in a game in which two drivers drive towards each other on a collision course: one must swerve, or both may die in the crash, but if one driver swerves but the other does not, s/he will be called a "chicken"; this terminology is most prevalent in the political science and economics. 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 biology and evolutionary game theory. From a game-theoretic point of view, "Chicken" and "Hawk-Dove" are identical; the different names stem from parallel development of the basic principles in different research areas.[1] The game has also been used to describe the mutually assured destruction of nuclear warfare. 

The game is similar to the prisoner's dilemma game in that an "agreeable" mutual solution is unstable since both players are individually tempted to stray from it. However, it differs in the cost of responding to such a deviation. This means that, even in an iterated version of the game, retaliation is ineffective, and a mixed strategy may be more appropriate. ... Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns. ... The Politics series Politics Portal This box:      Political Science is the field concerning the theory and practice of politics and the description and analysis of political systems and political behaviour. ... ‹ The template below is being considered for deletion. ... Biology studies the variety of life (clockwise from top-left) E. coli, tree fern, gazelle, Goliath beetle Biology (from Greek: βίος, bio, life; and λόγος, logos, knowledge), also referred to as the biological sciences, is the study of living organisms utilizing the scientific method. ... Evolutionary game theory (EGT) is the application of game theory in evolutionary biology. ... Mutually assured destruction (MAD) is the doctrine of military strategy in which a full scale use of nuclear weapons by one of two opposing sides would result in the destruction of both the attacker and the defender. ... This article is about nuclear war as a form of actual warfare, including history. ... Will the two prisoners cooperate to minimize total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In game theory, the prisoners dilemma (sometimes abbreviated PD) is a type of non-zero-sum game in which two players... In game theory a mixed strategy is a strategy which chooses randomly between possible moves. ...

Popular versions

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 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 his best outcome, risks the worst. A similar version, under the name of "chickie run", is a central plot element in the movie Rebel Without a Cause where the characters played by James Dean and Corey Allen race their cars towards a cliff instead of each other.^[2] Natalie Wood and James Dean in a screenshot from Rebel Without a Cause. ... For the film, see James Dean (film). ... Corey Allen (born Alan Cohen on June 29, 1934 in Cleveland, Ohio, USA) is an American film and television director, writer, producer and actor. ...

The phrase game of Chicken 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. Bertrand Russell famously compared the game of Chicken to nuclear brinkmanship: Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... This article is about nuclear war as a form of actual warfare, including history. ... This article or section does not adequately cite its references or sources. ...

Since the nuclear stalemate became apparent, the Governments of East and West have adopted the policy which Mr. Dulles calls 'brinkmanship'. This is a policy adapted from a sport which, I am told, is practised 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 towards each other from opposite ends. Each car is expected to keep the wheels of one side on 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 he passes, 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 is come, the statesmen of both sides will plunge the world into destruction.^[3]

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.^[4] In the "chickie run" scene this happens when Corey Allen's character cannot detach himself from the car and dies in the crash. The basic game-theoretic formulation of Chicken has no element of risk, and is also the contraction of a dynamic situation into a one-shot interaction.

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.^[5] They can use threat displays (play Dove), or physically attack each other (play Hawk). If both players choose the Hawk 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.

Game theoretic applications

Chicken

A formal version of the game of Chicken has been the subject of serious research in game theory.^[6] Two versions of the payoff matrix 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 numerical payoffs which conform to this situation. Here the benefit of winning is 1, the cost of losing is -1, and the cost of crashing is -10. It has been suggested that this article or section be merged with normal form game. ... A payoff matrix or payoff function is a concept in game theory which shows what payoff each player will receive at the outcome of the game. ... Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns. ... It has been suggested that this article or section be merged with normal form game. ...

Both "Chicken" and "Hawk-Dove" are anti-coordination games, 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 coordination game, where playing the same strategy Pareto dominates 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 non-rivalrous, and the shared usage creates positive externalities. In anti-coordination games the resource is rivalrous but non-excludable and sharing comes at a cost (or negative externality). In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... Pareto efficiency, or Pareto optimality, is an important notion in neoclassical economics with broad applications in game theory, engineering and the social sciences. ... In economics, something is considered rivalrous if its consumption by one person prevents it from being available to someone else. ... In economics, an externality is a cost or benefit resulting from an economic transaction that is borne or received by parties not directly involved in the transaction. ... Non-excludable goods are defined in economics as goods whereby it is impossible to stop a person consuming that good when it has become publicly available at a relatively low cost. ...

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 he will be reasonable and decide to swerve, leaving the other player the winner. This unstable situation can be formalized by saying there is more than one Nash equilibrium, which is a pair of strategies for which neither player gains by changing his own strategy while the other stays the same. (In this case, the pure strategy equilibria are the two situations wherein one player swerves while the other does not.) In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ... A pure strategy is a term used to refer to strategies in Game theory. ...

Hawk-Dove

In the biological literature, this game is referred to as Hawk-Dove. The earliest presentation of a form of the Hawk-Dove game was by John Maynard Smith and George Price in their 1973 Nature paper, "The logic of animal conflict".^[7] The traditional ^[5][8] payoff matrix 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 is, i.e., C > V > 0. If C ≤ V, the resulting game is not a game of Chicken. Professor John Maynard Smith[1], F.R.S. (6 January 1920 – 19 April 2004) was a British evolutionary biologist and geneticist. ... George R. Price (1922 - January 6, 1975) was a American population geneticist. ... Nature is one of the most prominent scientific journals, first published on 4 November 1869. ... It has been suggested that this article or section be merged with normal form game. ...

The exact value of the Dove vs. Dove playoff 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 war of attrition game, which is the presumed models for a contest decided by display duration). In game theory the War of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while accumulating costs at a constant rate c. ...

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.^[8]

Hawk-Dove variants

Biologists have explored modified versions of classic Hawk-Dove game to investigate a number of biologically relevant factors. These include adding variation in resource holding potential, and differences in the value of winning to the different players,^[9] allowing the players to threaten each other before choosing moves in the game,^[10] and extending the interaction to two plays of the game.^[11] In biology resource holding potential (RHP) is the ability of an animal to win an all-out fight were one to take place. ...

Pre-commitment

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 ^[12]. This shows that, in some circumstances, reducing one's own options can be a good strategy. One real-world example is a protester who handcuffs himself to an object, so that no threat can be made which would compel him to move (since he cannot move). Another example, taken from fiction, is found in Stanley Kubrick's Dr. Strangelove. In that film, the Russians sought to deter American attack by building a "doomsday machine," a device that would trigger world annihilation if Russia was hit by nuclear weapons.^[13] However, the Russians failed to signal — they deployed their doomsday machine covertly. “Kubrick” redirects here. ... Strangelove redirects here. ...

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 wastefully costly if the threat is one of two possible signals ("I will not swerve"/"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 "Rock, Paper, Scissors").^[10] The handicap principle is an idea proposed by the Israeli biologist Amotz Zahavi. ... Rock, Paper, Scissors chart Listen to this article ( info) in media player in browser This audio file was created from an article revision dated 2006-07-13, and may not reflect subsequent edits to the article. ...

Best response mapping and Nash equilibria

Fig.5 - Reaction correspondences for both players in a discoordination game. Compare with replicator dynamic vector fields below

All anti-coordination games have three Nash equilibria. Two of these are pure 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 mixed equilibrium, in which the each player probabilistically chooses between the two pure strategies. Either the pure, or mixed, Nash equilibria will be evolutionarily stable strategies depending upon whether uncorrelated asymmetries exist. Image File history File links Reaction-correspondence-hawk-dove. ... Image File history File links Reaction-correspondence-hawk-dove. ... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... A pure strategy is a term used to refer to strategies in Game theory. ... In game theory a mixed strategy is a strategy which chooses randomly between possible moves. ... Probability is the likelihood that something is the case or will happen. ... The evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a central concept in game theory introduced by John Maynard Smith and George R. Price in 1973 (a full account is given by Maynard Smith, 1982). ... In game theory an uncorrelated asymmetry is an informational asymmetry in a game which is otherwise symmetrical. ...

The best response mapping for all 2x2 anti-coordination games is shown in Figure 5. The variables x and y 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 x. The line in the second graph shows the optimum probability of playing the escalated strategy for player X as a function of y (not the axes have not been rotated, and so the dependent variable is plotted on the abscissa, and the independent variable is plotted on the ordinate). 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 evolutionarily stable strategy (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. In game theory, the best response, is the strategy (or strategies) which produces the most favorable immediate outcome for the current player, taking other players strategies as given. ... In experimental design, a dependent variable (also known as response variable, responding variable or regressand) is a factor whose values in different treatment conditions are compared. ... Abscissa means the x coordinate on an (x, y) graph; the input of a mathematical function against which the output is plotted. ... In an experimental design, the independent variable (argument of a function, also called a predictor variable) is the variable that is manipulated or selected by the experimenter to determine its relationship to an observed phenomenon (the dependent variable). ... Ordinate means the y coordinate on an (x, y) graph; the plotted output of a mathematical function. ... In game theory, an evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a strategy which if adopted by a population cannot be invaded by any competing alternative strategy. ...

Strategy polymorphism vs strategy mixing

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 instictive reactions for a single situation) or whether the population is a 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.^[14]

Symmetry breaking

In both "Chicken" and "Hawk-Dove", the only symmetric Nash equilibrium is the mixed strategy 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 contexts, with almost identical results.^[15] In game theory, a symmetric equilibrium is an equilibrium where both players use the same strategy (possibly mixed) in the equilibrium. ... In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ... In game theory a mixed strategy is a strategy which chooses randomly between possible moves. ...

Correlated equilibrium and Chicken

Consider the version of "Chicken" pictured in Figure 6. Like all forms of the game, there are three Nash equilibria. The two pure strategy Nash equilibria are (D, C) and (C, D). There is also a mixed strategy equilibrium where each player Dares with probability 1/3. In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... A pure strategy is a term used to refer to strategies in Game theory. ... In game theory a mixed strategy is a strategy which chooses randomly between possible moves. ...

Now consider a third party (or some natural event) that draws one of three cards labeled: (C, C), (D, C), and (C, D). After drawing the card the third party informs the players of the strategy assigned to them on the card (but not the strategy assigned to their opponent). Suppose a player is assigned D, he would not want to deviate supposing the other player played their assigned strategy since he will get 7 (the highest payoff possible). Suppose a player is assigned C. Then the other player will play C with probability 1/2 and D with probability 1/2. The expected utility 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. The expected utility hypothesis is the hypothesis in economics that the utility of an agent facing uncertainty is calculated by considering utility in each possible state and constructing a weighted average. ...

Since neither player has an incentive to deviate, this probability distribution over the strategies is known as a correlated equilibrium 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. In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. ...

Uncorrelated asymmetries and solutions to the Hawk-Dove game

Although there are three Nash equilibria in the Hawk-Dove game, the one which emerges as the evolutionarily stable strategy (ESS) depends upon the existence of any uncorrelated asymmetry in the game (in the sense of anti-coordination games). 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. In game theory, an evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a strategy which if adopted by a population cannot be invaded by any competing alternative strategy. ... In game theory an uncorrelated asymmetry is an informational asymmetry in a game which is otherwise symmetrical. ... In game theory, the best response, is the strategy (or strategies) which produces the most favorable immediate outcome for the current player, taking other players strategies as given. ...

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 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.^[15]

Replicator dynamics

Fig 7a: Vector field for two population replicator dynamics and Hawk-Dove

Replicator dynamics is a simple model of strategy change commonly used in evolutionary game theory. 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). Image File history File links Size of this preview: 600 × 600 pixelsFull resolution (1100 × 1100 pixel, file size: 158 KB, MIME type: image/png) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Size of this preview: 600 × 600 pixelsFull resolution (1100 × 1100 pixel, file size: 158 KB, MIME type: image/png) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... The replicator equation is a differential equation that defines the dynamics of evolutionary games. ... Evolutionary game theory (EGT) is the application of game theory in evolutionary biology. ...

In the one population model, the only stable state is the mixed strategy Nash equilibrium. Every initial population proportion (except all Hawk and all Dove) converge to the mixed strategy Nash Equilibrium where part of the population plays Hawk and part of the population plays Dove. (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 Hawks and the other of all Doves. In this model one population becomes the aggressive population while the other becomes passive. This model is illustrated by the vector field 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. Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ...

Fig. 7b: Vector field for single population replicator dynamics

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 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 version of the replicator dynamics differ wildly.^[16] Image File history File links Size of this preview: 800 × 54 pixelsFull resolution (1344 × 90 pixel, file size: 13 KB, MIME type: image/png) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Size of this preview: 800 × 54 pixelsFull resolution (1344 × 90 pixel, file size: 13 KB, MIME type: image/png) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

Related games

Prisoner's dilemma

"Chicken" and "Prisoner's dilemma" share the premise of a mutually agreeable, "compromise" solution (C, C) that is threatened by a Pareto dominated, "aggressive" solution (A, A). The threat comes from the fact each player is individually better off switching to A if the other player plays C, but if both switch they end up in (A, A). The games differ in their response to one player switching individually. Assuming player 1 chooses A, the best response in "Prisoner's dilemma" for player 2 is to switch to A as well, while in "Chicken" player 2 is better off remaining in C: "Prisoner's dilemma" allows player 2 to retaliate while "Chicken" does not. This has consequences if the game is played repeatedly: in the iterated prisoner's dilemma it is possible for (C, C) to be stable if the threat of retaliation is credible, while in iterated game of chicken, a stable compromise can only be achieved through brinkmanship. Will the two prisoners cooperate to minimize total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In game theory, the prisoners dilemma (sometimes abbreviated PD) is a type of non-zero-sum game in which two players... Pareto efficiency, or Pareto optimality, is an important notion in neoclassical economics with broad applications in game theory, engineering and the social sciences. ... In game theory, the best response, is the strategy (or strategies) which produces the most favorable immediate outcome for the current player, taking other players strategies as given. ... For other uses, see Revenge (disambiguation). ... Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? The prisoners dilemma is a type of non-zero-sum game. ...

Brinkmanship

"Chicken" and "Brinkmanship" are often used synonymously in the context of conflict, but in the strict game-theoretic sense, "brinkmanship" refers to a strategic move 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 (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. This article or section does not adequately cite its references or sources. ... A strategic move in game theory is an action taken by a player outside the defined actions of the game in order to gain a strategic advantage and increase ones payoff. ...

War of attrition

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 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. In game theory the War of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while accumulating costs at a constant rate c. ...

See also

• Coordination game
• Matching pennies
• Volunteer's dilemma

In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... Matching Pennies is the name for a simple example game used in game theory. ... The Volunteers dilemma game models a situation in which each of N players faces the decision of either making a small sacrifice from which all will benefit or freeriding. ...

Notes

Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era. ... is the 119th day of the year (120th in leap years) in the Gregorian calendar. ...

References

• Bergstrom, C.T. and Godfrey-Smith, P. (1998). "On the evolution of behavioral heterogeneity in individuals and populations". Biology and Philosophy 13: 205–231. 
• Cressman, R. (1995). "Evolutionary Stability for Two-stage Hawk-Dove Games". Rocky Mountain Journal of Mathematics 25: 145–155. 
• Deutsch, M. (1974). The Resolution of Conflict: Constructive and Destructive Processes. Yale University Press, New Haven. ISBN 978-0300016833. 
• Dixit, A.K. and Nalebuff, B.J. (1991). Thinking Strategically. W.W. Norton. ISBN 0393310353. 
• Fink, E.C., Gates, S., Humes, B.D. (1998). Game Theory Topics: Incomplete Information, Repeated Games, and N-Player Games. Sage. ISBN 0761910166. 
• Hammerstein, P. (1981). "The Role of Asymmetries in Animal Contests". Animal Behavior 29: 193–205. 
• Kahn, H. (1965). On escalation: metaphors and scenarios. Praeger Publ. Co., New York. ISBN 978-0313251634. 
• Kim, Y-G. (1995). "Status signaling games in animal contests". Journal of Theoretical Biology 176: 221–231. 
• Osborne, M.J. and Rubenstein, A. (1994). A course in game theory. MIT press. ISBN 0-262-65040-1. 
• Maynard Smith, J. (1982). Evolution and the Theory of Games. Cambridge University Press. ISBN 978-0521288842. 
• Maynard Smith, J. and Parker, G.A. (1976). "The logic of asymmetric contests". Animal Behaviour 24: 159–175. 
• Maynard Smith, J. and Price, G.R. (1973). "The logic of animal conflict". Nature 246: 15–18. 
• Moore, C.W. (1986). The Mediation Process: Practical Strategies for Resolving Conflict. Jossey-Bass, San Francisco. ISBN 978-0875896731. 
• Rapoport, A. and Chammah, A.M. (1966). "The Game of Chicken". American Behavioral Scientist 10. 
• Russell, B.W. (1959). Common Sense and Nuclear Warfare. George Allen and Unwin, London. ISBN 0041720032. 
• Skyrms, Brian (1996). Evolution of the Social Contract. New York: Cambridge University Press. ISBN 0521555833. 
• Weibull, Jörgen W. (1995). Evolutionary Game Theory. Cambridge, MA: MIT Press. ISBN 0-262-23181-6. 

Ariel Rubinstein (born April 13, 1951) is an economist who works in game theory. ... Professor John Maynard Smith[1], F.R.S. (6 January 1920 – 19 April 2004) was a British evolutionary biologist and geneticist. ... Book cover Evolution and the Theory of Games is a 1982 book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. ... Professor John Maynard Smith[1], F.R.S. (6 January 1920 – 19 April 2004) was a British evolutionary biologist and geneticist. ... Professor Geoffrey Alan Parker FRS (born 24 May 1944) is a professor of biology at the University of Liverpool. ... Professor John Maynard Smith[1], F.R.S. (6 January 1920 – 19 April 2004) was a British evolutionary biologist and geneticist. ... George R. Price (1922 - January 6, 1975) was a American population geneticist. ... Nature is one of the most prominent scientific journals, first published on 4 November 1869. ... Anatol Rapoport (born May 22, 1911) is a Russian-born American Jewish, mathematical psychologist. ... Brian Skyrms is a Distinguished Professor of Logic and Philosophy of Science and Economics at the University of California, Irvine. ...

External links

• The game of Chicken as a metaphor for human conflict
• Game-theoretic analysis of Chicken
• Game of Chicken – Rebel Without a Cause by Elmer G. Wiens.