Question

what are the nash equilibria in this game? instructions: in order to receive full credit, you must make a selection for each option. for correct answer(s), click the box once to place a check mark. for incorrect answer(s), click the option twice to empty the box.

Answer 1

For Player 1, only "A if W" and "B if Y" are feasible strategies. They guarantee at least 50 and 0 payoff respectively, no matter Player 2's move.

A if W: This strategy says that Player 1 will always play A if they reach the information set where they know it's their turn and the previous move was W. This is feasible because, regardless of what Player 2 does at the first decision node, Player 1 will always get a payoff of at least 50 if they play A in this information set. This is because:

If Player 2 plays W, then Player 1 gets (60, 120) if they play A and (50, 50) if they play B. So, playing A is at least as good as playing B.

If Player 2 plays Y, then Player 1 gets (50, 50) if they play A and (0, 0) if they play B. Again, playing A is at least as good as playing B.

B if Y: This strategy says that Player 1 will always play B if they reach the information set where they know it's their turn and the previous move was Y. This is feasible because, regardless of what Player 2 does at the first decision node, Player 1 will always get a payoff of at least 0 if they play B in this information set. This is because:

If Player 2 plays W, then Player 1 gets (60, 120) if they play A and (0, 0) if they play B. So, playing B is at least as good as playing A.

If Player 2 plays Y, then Player 1 gets (50, 50) if they play A and (0, 0) if they play B. Again, playing B is at least as good as playing A.

The other two strategies, A if X and B, are not feasible.

A if X: This strategy tells Player 1 to play A if they reach the information set where they know it's their turn and the previous move was X. However, there is no such information set in the game. So, this strategy is not feasible.

B: This strategy simply says that Player 1 will always play B. However, this is not feasible because in the information set where Player 1 knows it's their turn and the previous move was W, playing A would give them a higher payoff (60) than playing B (50).

Therefore, the only feasible strategies for Player 1 are A if W and B if Y.

For Player 1, both A if W and B if Y are feasible strategies.