Refer to the normal-form game of price competition shown below. Which of the following represents the set of possible pure strategy Nash equilibria?
A) {A, C}
B) {A, B}
C) {(A,
C), (A,
D), (B,
C), (B,
D)}
D) {C, D}

Question

Refer to the normal-form game of price competition shown below.  Which of the following represents the set of possible pure strategy Nash equilibria?
A) {A, C} 
B) {A, B} 
C) {(A, 
C), (A, 
D), (B, 
C), (B, 
D)} 
D) {C, D}

Quizplus · Accepted Answer

To find the pure strategy Nash equilibria, we need to identify any combination of strategies where no player has an incentive to unilaterally deviate, i.e. change their strategy. In this game, (A, C), (A, D), (B, C), and (B, D) are all potential Nash equilibria because in each case, neither player has an incentive to change. However, (A, B) is not a Nash equilibrium because in this case, player 2 would have an incentive to switch to strategy C, which would earn them a higher payoff. Option D is also incorrect because both players in this Nash equilibrium would have an incentive to switch to strategy A. Therefore, the correct answer is C, which represents all possible pure strategy Nash equilibria.

Refer to the Normal-Form Game of Price Competition Shown Below