Two players are engaged in a game of Chicken. There are two possible strategies, Swerve and Drive Straight. A player who chooses to Swerve is called Chicken and gets a payoff of zero, regardless of what the other player does. A player who chooses to Drive Straight gets a payoff of 36 if the other player swerves and a payoff of -36 if the other player also chooses to Drive Straight. This game has two pure strategy equilibria and
A) a mixed strategy equilibrium in which each player swerves with probability .50 and drives straight with probability .50.
B) a mixed strategy equilibrium in which one player swerves with probability .50 and the other swerves with probability .50.
C) a mixed strategy in which each player swerves with probability .25 and drives straight with probability .75.
D) two mixed strategies in which players alternate between swerving and driving straight.
E) no mixed strategies.

Question

Quizplus · Accepted Answer

The two pure strategy equilibria are when both players either choose to Swerve or Drive Straight. However, in a game of Chicken, both players have an incentive to choose Drive Straight in order to show that they are more courageous than the other player. Therefore, there is a possibility of both players choosing to Drive Straight, which results in a negative payoff for both players. The mixed strategy equilibrium in which each player Swerves with probability .50 and Drives Straight with probability .50 helps to mitigate the risk of both players choosing to Drive Straight and ensures that the players don't end up with a negative payoff. This makes A the best choice.

Two Players Are Engaged in a Game of Chicken