Question

Solve the following static game in normal form with complete information. Explain what method you used. Is the predicted equilibrium unique? Is it Pareto efficient? Why or why not? Show your work.

	L	C	R
U	3, 4	1, 2	0, 3
M	1, 5	4, 8	6, 9
D	2, 6	6, 3	8, 2

Answer 1

We will use the best response strategies to solve for the Nash equilibrium:

Best response of player 1:

Player 1 chooses U when player 2 chooses L

Player 1 chooses D when player 2 chooses C

Player 1 chooses D when player 2 chooses R

Best response of player 2:

Player 2 chooses L when player 1 chooses U

Player 2 chooses R when player 1 chooses M

Player 2 chooses L when player 1 chooses D

Thus, from the best responses, it is clear that there is a unique Nash equilibrium in which Player 1 chooses U and player 2 chooses L.

No, this is not Pareto efficient as the point (M, C) gives more payoff to both player 1 and player 2 and will thus pareto dominate the point (U, L)