What are the pure-strategy Nash equilibria of the following game?
A)Both play A.
B)Both play B.
C)Two equilibria: both play B in one and both play C in the other.
D)Two equilibria: 1 plays B and 2 plays A and vice versa.

Question

What are the pure-strategy Nash equilibria of the following game? 
A)Both play A. 
B)Both play B. 
C)Two equilibria: both play B in one and both play C in the other. 
D)Two equilibria: 1 plays B and 2 plays A and vice versa.

Quizplus · Accepted Answer

In a pure-strategy Nash equilibrium, each player is doing the best they can given the other player's choices. In this game, if Player 1 plays A, Player 2 is better off playing B (2 > 1). If Player 1 plays B, Player 2 is better off playing C (3 > 1). If Player 1 plays C, Player 2 is still better off playing C (2 > 0). Similarly, if Player 2 plays A, Player 1 is better off playing B (2 > 1), while if Player 2 plays B or C, Player 1 is better off playing C (3 > 1, 2 > 0). Thus, there are two Nash equilibria, where both players choose either B or C, depending on which equilibrium is played.

What Are the Pure-Strategy Nash Equilibria of the Following Game