Chicken (game)
From Wikipedia, the free encyclopedia
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For other uses, see Chicken (disambiguation).
Chicken is a game in which two players drive cars at each other. The first to swerve away and slow down loses and is humiliated as the "chicken"; if neither player swerves, the result is a potentially fatal head-on collision. The principle of the game is to create pressure until one person backs down.
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.
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[edit] 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, 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 equilibria are the two situations wherein one player swerves while the other does not.)
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). Another example, taken from fiction, is found in Stanley Kubrick's Dr. Strangelove. In that film, the Russians build a "doomsday machine," a device that would trigger world annihilation once Russia was to be hit by nuclear weapons. That way, they sought to deter any American attack. While in the movie the Russians deploy their doomsday machine covertly, thus failing to signal, the plotline does highlight the importance of signalling for understanding Chicken.
The payoff matrix for the game of chicken looks like this:
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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.
[edit] 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.
[edit] 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:
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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 value of the resource is less than the cost of a fight is, i.e. 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.
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):
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I J I a, a b, c J c, b d, d
where a<c, and d<b.
[edit] Uncorrelated asymmetries and solutions to the Hawk Dove game
The Hawk Dove game has three Nash equilibria:
- the row player chooses Hawk while the column player chooses Dove,
- the row player chooses Dove while the column player chooses Hawk, and
- 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.
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.
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.
[edit] See also
[edit] 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.
[edit] External links
- The game of chicken as a metaphor for human conflict
- Game-theoretic analysis of the game of chicken
- Game of Chicken - Rebel Without a Cause by Elmer G. Wiens.
| Topics in game theory | |
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Definitions |
Normal form game · Extensive form game · Cooperative game · Information set · Preference |
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Nash equilibrium · Subgame perfection · Bayes-Nash · Trembling hand · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy |
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Dominant strategies · Mixed strategy · Grim trigger · Tit for Tat |
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Classes of games |
Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design |
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Prisoner's dilemma · Coordination game · Chicken · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game |
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Theorems |
Minimax theorem · Purification theorems · Folk theorem · Revelation principle |
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Related topics |
Mathematics · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists |
