(See Problem 3.) 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 15.43 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) two mixed strategies in which players alternate between swerving and driving straight.
B) a mixed strategy in which each player swerves with probability 0.35 and drives straight with probability 0.65.
C) a mixed strategy equilibrium in which one player swerves with probability 0.70 and the other swerves with probability 0.30.
D) a mixed strategy equilibrium in which each player swerves with probability 0.70 and drives straight with probability 0.30.
E) no mixed strategies.

Question

Quizplus · Accepted Answer

Since there are two pure strategy equilibria, players could choose to both Swerve or both Drive Straight. However, if one player chooses to Drive Straight, the other player's best response is to Swerve to avoid getting a payoff of zero. Therefore, it is unlikely that both players will Drive Straight in the game.

To find the mixed strategy equilibrium, we can use the formula: 
p(Drive Straight) = (payoff of Swerve - payoff of Drive Straight) / (payoff of Swerve - payoff of Drive Straight + payoff of Swerve when opponent Drives Straight - payoff of Swerve when opponent Swerves)

Using the given payoffs, we have: 
p(Drive Straight) = (0 - (-36)) / (0 - (-36) + 15.43 - 0) = 36 / 51.43 = 0.70

This means that each player should choose to Swerve with probability 0.30 and Drive Straight with probability 0.70 in the mixed strategy equilibrium. Therefore, the answer is D.