http://www.egwald.ca/operationsresearch/chickengame.php

The link above describes a variation of the Hawk/Dove game theory, as presented in a popular James Dean movie. In this game, there is no dominant strategy for each player. Two people drive their cars towards a cliff or each other; the first person to jump out is the chicken, while the last is the “hero”. Therefore, the four outcomes are chicken, hero (and vice versa) and death for both players, which is a highly undesirable outcome. This game was also compared to nuclear brinkmanship since an element of uncontrollable risk is introduced.

The game of chicken differs from games such as the prisoner’s dilemma because both players do not have a dominant strategy, and there is a disparity in cost. Jumping at the same time gives both players a favourable outcome, but the payoff is very low. Player preference ranks being the hero over tying, tying over being the chicken, and being the chicken over crashing. Since both players would use different strategies for their best outcomes, this is an anti-coordination game, like the Hawk/Dove game theory that we covered in class. On the other hand, it shares similarities with the prisoner’s dilemma game because the mutual solution is often unstable, causing both players to avoid it.

An equilibrium for this game utilizes mixed strategies, which is most appropriate due to the anti-coordination. The players randomize their strategy choice and there is a probability of playing each strategy. The expected payoffs then for each player in this equilibrium would be in fraction form, since it factors in the probability of each eventual outcome. Neither player can “improve” the strategy despite changing their choices because of the unstable situation. There is no one Nash equilibrium. However, each player can harm the other by choosing not to be the chicken. When this happens, the least desirable outcome (death) occurs. So….try not to play this game.