To solve for a mixed-strategy equilibrium in a two-player, two-strategy game (two-by-two game):
A) set the expected value of playing the first strategy for the first player equal to the expected value of playing the first strategy for the second player, and solve for the implied probability.
B) always set the probability half to the first strategy and half to the second strategy.
C) for each player, roll a die to assign the probability of the first strategy and then calculate the implied second probability using the formula that probabilities must sum to one.
D) for each player, set the expected value of playing the first strategy equal to the expected value of playing the second strategy and solve for the implied probabilities.

Question

Quizplus · Accepted Answer

To find a mixed-strategy Nash equilibrium in a two-player, two-strategy game, you set the expected utility of playing the first strategy equal to the expected utility of playing the second strategy for each player. This process determines the probabilities with which each player should randomize over their strategies to keep the other player indifferent between their strategies, ensuring no player has an incentive to deviate unilaterally.

To Solve for a Mixed-Strategy Equilibrium in a Two-Player, Two-Strategy