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Chicken (game) - Wikipedia, the free encyclopedia
All anti-coordination games have three
Nash equilibria. Two of these are
pure contingent strategy profiles, in which each player plays one of the pair of strategies, and the other player chooses the opposite strategy. The third one is a
mixed equilibrium, in which each player
probabilistically chooses between the two pure strategies. Either the pure, or mixed, Nash equilibria will be
evolutionarily stable strategies depending upon whether
uncorrelated asymmetries exist.
The
best response mapping for all 2x2 anti-coordination games is shown in Figure 5. The variables
x and
y in Figure 5 are the probabilities of playing the escalated strategy ("Hawk" or "Don't swerve") for players X and Y respectively. The line in graph on the left shows the optimum probability of playing the escalated strategy for player Y as a function of
x. The line in the second graph shows the optimum probability of playing the escalated strategy for player X as a function of
y (the axes have not been rotated, so the
dependent variable is plotted on the
abscissa, and the
independent variable is plotted on the
ordinate). The Nash equilibria are where the players' correspondences agree, i.e., cross. These are shown with points in the right hand graph. The best response mappings agree (i.e., cross) at three points. The first two Nash equilibria are in the top left and bottom right corners, where one player chooses one strategy, the other player chooses the opposite strategy. The third Nash equilibrium is a mixed strategy which lies along the diagonal from the bottom left to top right corners. If the players do not know which one of them is which, then the mixed Nash is an
evolutionarily stable strategy (ESS), as play is confined to the bottom left to top right diagonal line.