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 3 if the other player Swerves and a payoff of 12 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 0.80 and drives straight with probability 0.20.
B) a mixed strategy equilibrium in which one player swerves with probability 0.80 and the other swerves with probability 0.20.
C) a mixed strategy in which each player swerves with probability 0.40 and drives straight with probability 0.60.
D) two mixed strategies in which players alternate between swerving and driving straight.
E) no mixed strategies.

In a game of chicken, both players have an incentive to not be the first one to swerve (i.e. to not show weakness). Therefore, both players have a dominant strategy to Drive Straight. However, if both players choose to Drive Straight, both get a payoff of 12, which is less than what they would get if they both chose to Swerve. Therefore, in order to avoid this outcome, each player wants to mix in some probability of Swerving. The Nash equilibrium is then found by solving for the probabilities that make each player indifferent between Swerving and Driving Straight. This results in the mixed strategy equilibrium where each player swerves with probability 0.80 and drives straight with probability 0.20. This equilibrium ensures that neither player has an incentive to deviate, because if one player deviates and chooses to Drive Straight with probability greater than 0.20, then the other player will start Swerving more often, leading to a lower payoff for the deviating player.