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Two players are playing Chicken. Each player may either choose to be a “chicken” or be “brave”. If both players choose “chicken”, the payoff to both players is 1. If both players choose to be “brave” the payoff is −2 to both players. Finally, if one player chooses to be “chicken” and the other player chooses to be “brave”, then the player choosing “brave” has payoff 2 and the player choosing “chicken” has payoff −1. Find three strategic equilibria.

The Payoff Matrix is $$\begin{bmatrix} & chicken & brave \\ chicken & (1,1) & (-1,2) \\ brave & (2,-1) & (-2,-2) \end{bmatrix}.$$ I think the equilibria strategis are (chicken, brave) and (brave, chicken ) . But I am not sure . Any help to find equilibrium?

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  • $\begingroup$ I see only these two equilibra, too. $\endgroup$ – Michael Hoppe May 30 '17 at 8:34
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You have found the two equilibria in pure strategies. The third equilibrium is in mixed strategies, with Player 1 and Player 2 both playing "chicken" or "brave" with equal probability, independently of each other.

In standard jargon, P1 plays chicken with probability $1/2$ and brave with probability $1/2$ and P2 does the same. The expected payoff to either player is $0$.

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