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 Swerve or both Drive Straight. However, in a mixed strategy equilibrium, both players must randomize between their strategies to ensure they each have an equal expected payoff.
To find the mixed strategy equilibrium, we can use the concept of indifference. If both players are indifferent between Swerving and Driving Straight, then they will randomize between the two strategies. 
For Player 1, they are indifferent when:
0 = p(Drive Straight)(-48) + (1-p)(32)
0 = -48p + 32 - 32p
16p = 32
p = 0.5
Similarly, for Player 2, they are indifferent when:
0 = q(Drive Straight)(-48) + (1-q)(32)
0 = -48q + 32 - 32q
16q = 32
q = 0.5
Therefore, in the mixed strategy equilibrium, each player will Swerve with probability 0.5 and Drive Straight with probability 0.5. This is equivalent to choice A.

Two Players Are Engaged in a Game of Chicken