User:Bwithh/parking

(tag removed) mergefrom|Peace war game|date=October 2006}} 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.

Chicken and game theory[edit]

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:

	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.

Chicken and the prisoner's dilemma[edit]

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.

Hawk-Dove game[edit]

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:

	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):

	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[edit]

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.

Nuclear chicken[edit]

In his 1959 book Common Sense and Nuclear Warfare[1], British philosopher Bertrand Russell famously compared the game of chicken with U.S. Secretary of State John Foster Dulles' policy of nuclear brinkmanship between the Cold War superpowers, the United States and the Soviet Union. Russell also argued though that the game was inadequate when assessing the stand-off between multiple nuclear-armed states.

References[edit]

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.

External links[edit]

Category:Game theory

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Definitions	Congestion game Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game
Equilibrium concepts	Bayes correlated equilibrium Bayesian Nash equilibrium Berge equilibrium Core Correlated equilibrium Epsilon-equilibrium Evolutionarily stable strategy Gibbs equilibrium Mertens-stable equilibrium Markov perfect equilibrium Nash equilibrium Pareto efficiency Perfect Bayesian equilibrium Proper equilibrium Quantal response equilibrium Quasi-perfect equilibrium Risk dominance Satisfaction equilibrium Self-confirming equilibrium Sequential equilibrium Shapley value Strong Nash equilibrium Subgame perfection Trembling hand
Strategies	Appeasement Backward induction Bid shading Collusion De-escalation Deterrence Escalation Forward induction Grim trigger Markov strategy Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat
Classes of games	Bargaining problem Cheap talk Global game Intransitive game Mean-field game Mechanism design n-player game Perfect information Large Poisson game Potential game Repeated game Screening game Signaling game Stackelberg competition Strictly determined game Stochastic game Symmetric game Zero-sum game
Games	Go Chess Infinite chess Checkers Tic-tac-toe Prisoner's dilemma Gift-exchange game Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Lewis signaling game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock paper scissors Pirate game Dictator game Public goods game Blotto game War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Induction puzzles Trust game Princess and monster game Rendezvous problem
Theorems	Arrow's impossibility theorem Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Negamax theorem Purification theorem Revelation principle Sprague–Grundy theorem Zermelo's theorem
Key figures	Albert W. Tucker Amos Tversky Antoine Augustin Cournot Ariel Rubinstein Claude Shannon Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin John Conway Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Axelrod Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey
Miscellaneous	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory First-move advantage in chess Glossary of game theory List of game theorists List of games in game theory No-win situation Solving chess Topological game Tragedy of the commons Tyranny of small decisions