Question

Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0, 0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players get O if the combination of actions is (B, R). What are the pure strategy Nash equilibria of the game? O (B, L) O (T, R) O (B, L) and (T, L) O (B, L) and (T, R) O None of the above

Answer 1

Option (4).

Payoff matrix as follows.

		Player 2
		L	R
Player 1	T	(0,    0)	(6,    2)
	B	(5,    7)	(0,    0)

When Player 1 chooses T, Player 2's best strategy is R since payoff is higher (2 > 0).

When Player 1 chooses B, Player 2's best strategy is L since payoff is higher (7 > 0).

When Player 2 chooses L, Player 1's best strategy is B since payoff is higher (5 > 0).

When Player 2 chooses R, Player 1's best strategy is T since payoff is higher (6 > 0).

So, Nash equilibria are: (B, L) and (T, R) [see below]

Player 2 R (0, 0) (6 2) т Player 1 (5,1 7(0, 0) В