Difference between revisions of "The Chicken Game"
(→Principles) |
(→Principles) |
||
| Line 21: | Line 21: | ||
Being chicken is the next to worst outcome, but still better than dying. | Being chicken is the next to worst outcome, but still better than dying. | ||
| − | 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 | + | 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. | + | 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== | ==Payoff matrix== | ||
Revision as of 01:25, 27 January 2013
Chicken game is also known as Game of Chicken, Chicken, Hawk-dove. Besides Prisoner's dilemma, Stag Hunt, Battle of the Sexes, Chicken game is one of well-known analysed games from Game theory.
Contents
History
The Chicken story comes from the deadly teenage game of the 1950s, in which two teens (or groups of teens) drove their cars straight at each other to find out who would flinch first. The first to grab the wheel and swerve "lost" by showing that s/he lacked courage. Nevertheless, if one swerved and the other didn't, as in the upper right and lower left comers, the joint welfare of both parties was at its highest: the "hawk" could preen in his or her show of valor, while even the losing "dove" or "chicken" would still be alive, if embarrassed. The worst case, of course, was when nobody swerved and the cars crashed (lower right corner). If both swerved (upper left), the crash would not occur, but no one would be able to claim bravery, so that the "resource" of preening would go unexploited. Thus in Chicken as in Battle of the Sexes, there are two jointly maximizing results, but those results have unequal payoffs to the two players. The difference is that in Battle of the Sexes, the jointly maximizing solutions require both parties to follow a single strategy, even though one prefers it and the other does not. In Chicken, on the other hand, the parties must choose opposite strategies, with one deferring to the other to avoid the crash, while the other drives through and claims the reward [1].
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 [2].
‘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].
Principles
Chicken readily translates into an abstract game. Strictly speaking, game theory's chicken dilemma occurs at the last possible moment of a game of highway chicken. Each driver has calculated his reaction time and his car's turning radius (which are assumed identical for both cars and both drivers); there comes a moment of truth in which each must decide whether or not to swerve. This decision is irrevocable and must be made in ignorance of the other driver's decision. There is no time for one driver's last-minute decision to influence the other driver's decision. In its simultaneous, life or death simplicity, chicken is one of the purest examples of von Neumann's concept of a game.
The way players rank outcomes in highway chicken is obvious. The worst thing that can happen is for both players not to swerve. Then – BAM!! – the coroner picks both out of a Corvette dashboard.
The best thing that can happen, the real point of the game, is to show your machismo by not swerving and letting the other driver swerve. You survive to gloat, and the other guy is "chicken."
Being chicken is the next to worst outcome, but still better than dying.
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 [2].
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)[2]..
| chicken/drive | swerve (chicken) | straight (drive) |
| swerve (chicken) | tie | lose,win |
| straight (drive) | win,lose | death |
| chicken/drive | swerve (chicken) | straight (drive) |
| swerve (chicken) | 0, 0 | -1, +1 |
| straight (drive) | +1, -1 | -100, -100 |
Chicken and Prisoner
Mutual defection (the crash when both players drive straight) is the most feared outcome in chicken. In the prisoner's dilemma, cooperation while the other player defects (being the sucker) is the worst outcome.
The players of a prisoner's dilemma are better off defecting, no matter what the other does. One is inclined to view the other player's decision as a given (possibly the other prisoner has already spilled his guts, and the police are withholding this information). Then the question becomes, why not take the course that is guaranteed to produce the higher payoff?
This train of thought is less compelling in chicken. The player of chicken has a big stake in guessing what the other player is going to do. A curious feature of chicken is that both players want to do the opposite of whatever the other is going to do. If you knew with certainty that your opponent was going to swerve, you would want to drive straight. And if you knew he was going to drive straight, you would want to swerve – better chicken than dead. When both players want to be contrary, how do you decide? [2].
References
- ↑ Rose, Carol M., "Game Stories" (2010). Faculty Scholarship Series. Paper 1728. online
- ↑ 2.0 2.1 2.2 2.3 POUNDSTONE, William. Prisoner´s dilemma. New York: Anchor Books, c1992, xi, 294 s. ISBN 03-854-1580-X. Cite error: Invalid
<ref>tag; name "poundstone" defined multiple times with different content Cite error: Invalid<ref>tag; name "poundstone" defined multiple times with different content Cite error: Invalid<ref>tag; name "poundstone" defined multiple times with different content - ↑ RUSSELL, Bertrand. Common sense and nuclear warfare. New York: Routledge, 2001, xxvii, 77 p. ISBN 04-152-4994-5.
