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Encyclopedia > Game of chicken

The game of chicken (also referred to as playing chicken) is a "game" in which two players engage in an activity that will result in serious harm unless one of them backs down. It is commonly applied to the use of motor vehicles whereby each drives a vehicle of some sort towards the other, and the first to swerve away and slow down loses and is humiliated as the "chicken". (An example of this can be seen in the movie Rebel Without a Cause, in which two characters drive towards a cliff.) In practice, this sort of game, if played at all, is most likely to be played amongst adolescents or aggressive young men, though it more often involves less severe risk, say two people might ride at each-other on bicycles. The principle of the game is to create pressure until one person backs down. Injury is damage or harm caused to the structure or function of the body caused by an outside agent or force, which may be physical or chemical. ... Chicken, used as a term of speech, means to call someone chicken, thereby meaning that they are afraid to do something. ... Natalie Wood and James Dean in a screenshot from Rebel Without a Cause. ... A separate article is about the punk band called The Adolescents. ...


The phrase game of chicken may also be 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, a method of negotiation in which each party delays making concessions until the deadline is imminent. The psychological pressure may force a negotiator to concede to avoid a negative outcome. It can be a very dangerous tactic; if neither party "swerves", a "crash" is certain to occur. Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was a British philosopher, logician, and mathematician, working mostly in the 20th century. ... The Titan II ICBM carried a 9 Mt W53 warhead, making it one of the most powerful nuclear weapons fielded by the United States during the Cold War. ... This article or section does not cite its references or sources. ... Negotiation is the process whereby interested parties resolve disputes, agree upon courses of action, bargain for individual or collective advantage, and/or attempt to craft outcomes which serve their mutual interests. ...

Contents


Chicken and game theory

A formal version of the game of chicken has been the subject of serious research in game theory. 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 strategy can be formalized by saying there is more than one Nash equilibrium for the game, a Nash equilibrium being a pair of strategies for which neither player gains by changing his own strategy while the other stays the same. (In this case, the equilibria are the two situations wherein one player swerves while the other does not.) Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ... In game theory, the Nash equilibrium (named after John Nash, who proposed it) is a kind of solution concepts of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ...


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 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).


The payoff matrix for the game of chicken looks like this: It has been suggested that this article or section be merged with normal form game. ...

Swerving Driving straight
Swerving 0, 0 -1, +1
Driving straight +1, -1 -100, -100

Of course, this model assumes that one chooses one's strategy before playing and sticks to it - an unrealistic assumption, since if a player sees the other swerving early, he can drive straight, no matter what his earlier plans.


This model also assumes that, if both parties swerve, they will not swerve in the same direction.


Under this model, and in contrast to the prisoner's dilemma, where one action is always best, in the game of chicken one wants to do the opposite of whatever the other player is doing. 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? Many points in this article may be difficult to understand without a background in the elementary concepts of game theory. ...


Chicken and the prisoner's dilemma

In chicken, if your opponent cooperates (swerves), you are better off to defect (drive straight) - this is your best possible outcome. If your opponent defects, you are better off to cooperate. Mutual defection is the worst possible outcome (hence unstable), but in the prisoner's dilemma the worst possible outcome is cooperating while the other player defects, and mutual defection is stable. In both games, mutual cooperation is unstable. 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? Many points in this article may be difficult to understand without a background in the elementary concepts of game theory. ...


Hawk-Dove game

The game is also known as the Hawk-Dove game in biological game theory. In this interpretation two players contesting an indivisible resource 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 strategy, they fight and injure each other. If only one player chooses hawk, then this player defeats the dove player. If both players play dove, there is a tie in profit, but the profit is lower than the profit of a hawk defeating a dove. In this biological setting, playing the dove or hawk strategy is analogous to cooperating or defecting respectively.


The traditional (Maynard Smith, 1982) payoff matrix for the Hawk-Dove game looks like this: John Maynard Smith Professor John Maynard Smith, F.R.S. (6 January 1920 – 19 April 2004) was a British evolutionary biologist and geneticist. ... It has been suggested that this article or section be merged with normal form game. ...

Hawk Dove
Hawk 1/2*(V-C), 1/2*(V-C) V, 0
Dove 0, V V/2, V/2

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 cost of a fight is more than the value of the resource, V<C. Were it not the case that V<C, then the game will not correspond to the game of chicken. A common payoff variant is to assume that the Dove vs. Dove outcome leads to a War of Attrition, for which the expected payoff is zero, and thus the V/2 payoffs are replaced with zeros. 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 (Maynard Smith, 1982):

I J
I a, a b, c
J c, b d, d

where a<c, and d<b.


Uncorrelated asymmetries and solutions to the Hawk Dove game

The Hawk Dove game has three Nash equilibria; 1) the row players chooses Hawk while the column player chooses Dove, 2) the row player chooses Dove while the column player chooses Hawk, and 3) both players play a mixed strategy where Hawk is played with probability p, and Dove is played with probability 1-p. It can be demonstrated that p=V/C in the traditional payoff version, and p=(b-d)/(b+c-a-d) in the generic payoff version. 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. ...


While there are three Nash equilibria, which will be evolutionarily stable strategies (ESSs) depends upon the existence of any uncorrelated asymmetry in the game (see also section on discoordination games in best response). 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. 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 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 in a single period that creates the most favorable immediate outcome for the current player, taking other players strategies as given. ...


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 contigent, Nash equilibria are.


See also

  • War of attrition (game)

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. ...

References

  • Deutsch, M. The Resolution of Conflict: Constructive and Destructive Processes. Yale University Press, New Haven, CT, 1973.
  • Maynard Smith, J. (1982) Evolution and the Theory of Games.
  • Moore, C. W. The Mediation Process: Practical Strategies for Resolving Conflict. Jossey-Bass, San Francisco, 1986.
  • Rapoport, A. (1966) The game of chicken, American Behavioral Scientist 10: 10-14.

John Maynard Smith Professor John Maynard Smith, 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. ... Anatol Rapoport (born May 22, 1911) is a Russian-born American Jewish, mathematical psychologist. ...

External links


v·d·e
Topics in game theory

Definitions Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...

Normal form game · Extensive form game · Cooperative game · Information set · Preference In game theory, normal form is a way of describing a game. ... It has been suggested that Game tree be merged into this article or section. ... A cooperative game is a game where groups of players (coalitions) may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players. ... In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed so far. ... Preference (or taste) is a concept, used in the social sciences, particularly economics. ...

Equilibrium concepts In economics, economic equilibrium often refers to an equilibrium in a market that clears: this is the case where a market for a product has attained the price where the amount supplied of a certain product equals the quantity demanded. ... In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...

Nash equilibrium · Subgame perfection · Bayes-Nash · Trembling hand · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy In game theory, the Nash equilibrium (named after John Nash, who proposed it) is a kind of solution concepts of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ... Subgame perfect equilibrium is an economics term used in game theory to describe an equilibrium such that players strategies constitute a Nash equilibrium in every subgame of the original game. ... In game theory, a Bayesian game is one in which information about characteristics of the other players (i. ... The trembling hand perfection is a notion that eliminates actions of players that are unsafe because they were chosen through a slip of the hand. ... In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. ... Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson. ... Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme. ... 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. ...

Strategies In game theory, a players strategy, in a game or a business situation, is a complete plan of action for whatever situation might arise; this fully determines the players behaviour. ...

Dominant strategies · Mixed strategy · Grim trigger · Tit for Tat In game theory, dominance (also called strategic dominance) occurs when one strategy is better than another strategy for one player, no matter how that players opponents may play. ... A mixed strategy is used in game theory economics to describe a strategy comprising possible moves and a probability distribution which corresponds to how frequently each move is chosen. ... Grim Trigger is a trigger strategy in game theory for a repeated game, such as an iterated prisoners dilemma. ... Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ...

Classes of games

Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. ... Perfect information is a term used in economics and game theory to describe a state of complete knowledge about the actions of other players that is instantaneously updated as new information arises. ... In game theory, a sequential game is a game where one player chooses his action before the others chooses theirs. ... In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ... Signaling games are dynamic games with two players, the sender (S) and the receiver (R). ... Cheap Talk is a term used in Game Theory for pre-play communication which carries no cost. ... Zero-sum describes a situation in which a participants gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). ... Mechanism design is a sub-field of game theory. ...

Games Game theory studies strategic interaction between individuals in situations called games. ...

Prisoner's dilemma · Chicken · Stag hunt · Ultimatum game · Coordination game · Matching pennies · Minority Game · Rock, Paper, Scissors · Pirate Game · Dictator game 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? Many points in this article may be difficult to understand without a background in the elementary concepts of game theory. ... In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. ... The Ultimatum game is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. ... 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. ... Minority Game is a game proposed by Yi-Cheng Zhang and Damien Challet from the University of Fribourg. ... Rock, Paper, Scissors chart Rock, Paper, Scissors, also known in Japan as Janken, is a hand game most often played by children. ... The Pirate Game is a simple mathematical game. ... The dictator game is a very simple game in experimental economics, similar to the ultimatum game. ...

Theorems

Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Bishop-Cannings theorem Minimax is a method in decision theory for minimizing the expected maximum loss. ... In game theory, the purification theorem was contributed by Nobel laurate John Harsanyi in 1973[1]. The theorem aims to justify a puzzling aspect of mixed strategy Nash equilibria: that each player is wholly indifferent amongst each of the actions he puts non-zero weight on, yet he mixes them... In game theory, folk theorems are a class of theorems which imply that in repeated games, any outcome is a feasible solution concept, if under that outcome the players minimax conditions are satisfied. ... In game theory, the Bishop-Cannings theorem proves that all members of a mixed evolutionarily stable strategy have the same payoff, and that none of these can also be a pure evolutionarily stable strategy. ...

Related topics

Mathematics · Economics · Behavioral economics · Evolutionary biology · Evolutionary game theory · Population genetics · Behavioral ecology · List of game theorists Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ... Buyers bargain for good prices while sellers put forth their best front in Chichicastenango Market, Guatemala. ... Nobel Prize in Economics winner Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ... Evolutionary biology is a subfield of population biology concerned with the origin and descent of species, as well as their change over time, i. ... Evolutionary game theory (EGT) is the application of game theory in evolutionary biology. ... Population genetics is the study of the distribution of and change in allele frequencies under the influence of the four evolutionary forces: natural selection, genetic drift, mutation, and migration. ... Behavioral ecology is the study of the ecological and evolutionary basis for animal behavior, and the roles of behavior in enabling an animal to adapt to its environment (both intrinsic and extrinsic). ... This is a list of notable economists, mathematicians, political scientists, and computer scientists whose work has added substantially to the field of game theory. ...


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