Question

2. In a two-player, one-shot, simultaneous-move game, each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $400. If both players choose strategy B, each earns a payoff of $200. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $100 and player 2 earns $600. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $600 and player 2 earns $100.

a. Write the above game in normal form.

b. Find each player’s dominant strategy, if it exists.

c. Find the Nash equilibrium (or equilibria) of this game.

d. Rank strategy pairs by aggregate payoff (highest to lowest).

e. Can the outcome with the highest aggregate payoff be sustained in equilibrium? Why or why not?

Answer 1

Q2) a) The above game can be represented in the normal form as :

PLAYER 2

	STRATEGY A	STRATEGY B
STRATEGY A	(400, 400)	(100,600)
STRATEGY B	(600,100)	(200,200)

b) If player 1 chooses strategy A, then player B will choose strategy B as it gives him a higher pay-off of 600 as compared to 400.

If player 1 chooses strategy B, then player 2 will choose strategy B as it gives him a higher pay-off of 200 as compared to 100.

So, the dominant strategy for player 2 is to choose strategy B.

If player 2 chooses strategy A, then player 1 will choose strategy B as it gives him a higher pay-off of 600 as compared to 400.

If player 2 chooses strategy B, then player 1 will choose strategy B as it gives him a higher pay-off of 200 as compared to 100.

So, dominant strategy for player 1 is to choose strategy B.

c)

If player 1 chooses strategy A, then player B will choose strategy B as it gives him a higher pay-off of 600 as compared to 400.

If player 1 chooses strategy B, then player 2 will choose strategy B as it gives him a higher pay-off of 200 as compared to 100.

If player 2 chooses strategy A, then player 1 will choose strategy B as it gives him a higher pay-off of 600 as compared to 400.

If player 2 chooses strategy B, then player 1 will choose strategy B as it gives him a higher pay-off of 200 as compared to 100.

So, nash equilibrium is determined at (200, 200) that is when both the players choose strategy B.

d) The aggregate pay-off is highest when players choose strategy (A, A) that is 400 + 400 = 800.

Then, second high pay-off is when the players choose strategy (A , B) or (B, A) that is 100 + 600 = 700 or 600 + 100 = 700.

The least pay-off is that of strategy (B,B) which is 200 + 200 = 400.