The Chicken Game - Revision history

Xmacm45: /* Payoff matrix */

2013-01-27T11:32:16Z

‎Payoff matrix

Xmacm45: /* Variations */

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‎Variations

Xmacm45: /* Evolutionary Game Theory */

2013-01-27T11:15:19Z

‎Evolutionary Game Theory

Xmacm45: /* Evolutionary Game Theory */

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‎Evolutionary Game Theory

Xmacm45: /* Principles */

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‎Principles

Xmacm45: /* Principles */

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‎Principles

Xmacm45: /* Nuclear stalemate */

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‎Nuclear stalemate

Xmacm45: /* Evolutionary Game Theory */

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‎Evolutionary Game Theory

Xmacm45: /* Evolutionary Game Theory */

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‎Evolutionary Game Theory

Xmacm45: /* Evolutionary Game Theory */

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‎Evolutionary Game Theory

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 ==Payoff matrix==
-The game of chicken has two Nash equilibriums (boldface, lower left and upper right cells). This is another case where the Nash theory leaves something to be desired. You don't want two solutions, any more than you want two heads. The equilibrium points are the cases where one player swerves and the other doesn't (lower left and upper right).<ref name="poundstone">William Poundstone, Prisoner's Dilemma, Doubleday, NY 1992</ref>
+The game of chicken has two [[Nash equilibrium]]s (boldface, lower left and upper right cells). This is another case where the Nash theory leaves something to be desired. You don't want two solutions, any more than you want two heads. The equilibrium points are the cases where one player swerves and the other doesn't (lower left and upper right).<ref name="poundstone">William Poundstone, Prisoner's Dilemma, Doubleday, NY 1992</ref>
 {| class="wikitable"

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 * The other driver is a remote-controlled dummy whose choice is made randomly. There is a 50 percent chance he will swerve and a 50 percent chance he will drive straight.
-The suicidal driver evidently can be counted on to drive straight (the possibly fatal strategy). You'd rationally have to swerve. The random driver illustrates another difference between chicken and the prisoner's dilemma. With an opponent you can't second-guess, you might be inclined to play it safe and swerve. Of the two strategies in chicken, swerving (cooperation) has the maximum minimum. In the prisoner's dilemma, defection is safer. <ref name="alexander">Alexander, J. McKenzie, "Evolutionary Game Theory", The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2009/entries/game-evolutionary/>. </ref>
+The suicidal driver evidently can be counted on to drive straight (the possibly fatal strategy). You'd rationally have to swerve. The random driver illustrates another difference between chicken and the prisoner's dilemma. With an opponent you can't second-guess, you might be inclined to play it safe and swerve. Of the two strategies in chicken, swerving (cooperation) has the maximum minimum. In the prisoner's dilemma, defection is safer. <ref name="poundstone">William Poundstone, Prisoner's Dilemma, Doubleday, NY 1992</ref>
 =Chicken and Prisoner=

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 ==Evolutionary Game Theory==
-There are two approaches to evolutionary game theory. The first approach derives from the work of Maynard Smith and Price and employs the concept of an <b>evolutionarily stable strategy</b> as the principal tool of analysis. The second approach constructs an explicit model of the process by which the frequency of strategies change in the population and studies properties of the evolutionary dynamics within that model.
+There are two approaches to evolutionary game theory. The first approach derives from the work of Maynard Smith and Price and employs the concept of an <b>evolutionarily stable strategy</b> as the principal tool of analysis. The second approach constructs an explicit model of the process by which the frequency of strategies change in the population and studies properties of the evolutionary dynamics within that model.<ref name="alexander">Alexander, J. McKenzie, "Evolutionary Game Theory", The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2009/entries/game-evolutionary/></ref>
 The first approach can thus be thought of as providing a static conceptual analysis of evolutionary stability. “Static” because, although definitions of evolutionary stability are given, the definitions advanced do not typically refer to the underlying process by which behaviours (or strategies) change in the population. The second approach, in contrast, does not attempt to define a notion of evolutionary stability: once a model of the population dynamics has been specified, all of the standard stability concepts used in the analysis of dynamical systems can be brought to bear.

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 Given this characterization of an evolutionarily stable strategy, one can readily confirm that, for the Hawk-Dove game, the strategy Dove is not evolutionarily stable because a pure population of Doves can be invaded by a Hawk mutant. If the value V of the resource is greater than the cost C of injury (so that it is worth risking injury in order to obtain the resource), then the strategy Hawk is evolutionarily stable. In the case where the value of the resource is less than the cost of injury, there is no evolutionarily stable strategy if individuals are restricted to following pure strategies, although there is an evolutionarily stable strategy if players may use mixed strategies.
-In the years following the original work of Maynard Smith and Price, alternate analytic solution concepts have been proposed. Of these, two important ones are the idea of an evolutionarily stable set (see Thomas 1984, 1985a,b), and the idea of a “limit ESS” (see Selten 1983, 1988). The former provides a setwise generalization of the concept of an evolutionarily stable strategy, and the latter extends the concept of an evolutionarily stable strategy to the context of two-player extensive form games<ref name="alexander">Alexander, J. McKenzie, "Evolutionary Game Theory", The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2009/entries/game-evolutionary/>.</ref>
+In the years following the original work of Maynard Smith and Price, alternate analytic solution concepts have been proposed. Of these, two important ones are the idea of an evolutionarily stable set (see Thomas 1984, 1985a,b), and the idea of a “limit ESS” (see Selten 1983, 1988). The former provides a setwise generalization of the concept of an evolutionarily stable strategy, and the latter extends the concept of an evolutionarily stable strategy to the context of two-player extensive form games.<ref name="alexander">Alexander, J. McKenzie, "Evolutionary Game Theory", The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2009/entries/game-evolutionary/></ref>
 =Variations=

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 There is a cooperative outcome in chicken. It's not so bad if both players swerve. Both come out alive, and no one can call the other a chicken. The payoff table might look like the following. The numbers represent arbitrary points, starting with 0 for the worst outcome, 1 for the next-to-worst outcome, and so on.
-The outcome where you drive straight and the other swerves is also an equilibrium point. What actually happens when this game is played? It's hard to say. Under Nash's theory, either of the two of the equilibrium points is an equally "rational" outcome. Each player is hoping for a different equilibrium point, and unfortunately the outcome may not be an equilibrium point at all. Each player can choose to drive straight – on grounds that it is consistent with a rational, Nash-equilibrium solution – and rationally crash <ref name="poundstone">William Poundstone, Prisoner's Dilemma, Doubleday, NY 1992</ref>.
+The outcome where you drive straight and the other swerves is also an equilibrium point. What actually happens when this game is played? It's hard to say. Under Nash's theory, either of the two of the equilibrium points is an equally "rational" outcome. Each player is hoping for a different equilibrium point, and unfortunately the outcome may not be an equilibrium point at all. Each player can choose to drive straight – on grounds that it is consistent with a rational, Nash-equilibrium solution – and rationally crash. <ref name="poundstone">William Poundstone, Prisoner's Dilemma, Doubleday, NY 1992</ref>
 ==Payoff matrix==

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 =Nuclear stalemate=
-Bertrand Russell saw in chicken a metaphor for the nuclear stalemate. His 1959 book, Common Sense and Nuclear Warfare, not only describes the game but offers mordant comments on those who play the geopolitical version of it. Incidentally, the game Russell describes is now considered the "canonical" chicken, at least in game theory, rather than the off-the-cliff version of the movie <ref name="poundstone">POUNDSTONE, William. Prisoner´s dilemma. New York: Anchor Books, c1992, xi, 294 s. ISBN 03-854-1580-X. </ref>.
+Bertrand Russell saw in chicken a metaphor for the nuclear stalemate. His 1959 book, Common Sense and Nuclear Warfare, not only describes the game but offers mordant comments on those who play the geopolitical version of it. Incidentally, the game Russell describes is now considered the "canonical" chicken, at least in game theory, rather than the off-the-cliff version of the movie <ref name="poundstone">POUNDSTONE, William. Prisoner´s dilemma. New York: Anchor Books, c1992, xi, 294 s. ISBN 03-854-1580-X. </ref>
 ‘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.’ <ref name="russell">RUSSELL, Bertrand. Common sense and nuclear warfare. New York: Routledge, 2001, xxvii, 77 p. ISBN 04-152-4994-5.</ref>.
+‘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.’ <ref name="russell">RUSSELL, Bertrand. Common sense and nuclear warfare. New York: Routledge, 2001, xxvii, 77 p. ISBN 04-152-4994-5.</ref>
 =Principles=