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 32 if the other player swerves and a payoff of -48 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 .60 and drives straight with probability .40.
B)two mixed strategies in which players alternate between swerving and driving straight.
C)a mixed strategy equilibrium in which one player swerves with probability .60 and the other swerves with probability .40.
D)a mixed strategy in which each player swerves with probability .30 and drives straight with probability .70.
E)no mixed strategies.

Question

Quizplus · Accepted Answer

The two pure strategy equilibria are when both players either choose to Swerve or both choose to Drive Straight. However, since the payoff for Swerving is always lower than the payoff for Driving Straight, it makes sense for both players to choose Driving Straight if they believe the other player will Swerve. Therefore, in a mixed strategy equilibrium, both players should choose to Drive Straight with some probability. By symmetry, they should choose the same probabilities for each strategy. The optimal probabilities can be found using the formula p(Drive Straight) = (payoff for driving straight when opponent drives straight - payoff for swerving) / (payoff for driving straight when opponent drives straight - payoff for driving straight when opponent swerves). Plugging in the numbers, we get p(Drive Straight) = (48 - 0) / (48 - 32) = 0.40. Therefore, each player should Swerve with probability 0.60 and Drive Straight with probability 0.40.

Two Players Are Engaged in a Game of Chicken