Question

1) Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs: Firm B - low output Firm B - high output Firm A - low output 300, 250 200, 100 Firm A - high output 200, 75 75, 100

a. What are the dominant strategies in this game? Do both players have them?

b. What is the Nash Equilibrium for this game?

Answer 1

The payoff matrix:

		Firm B
Firm A		Low	High
Low	300, 250	200, 100
	High	200, 75	75, 100

a. Dominant strategy of this game is Low output. Only firm A has it. Firm B has no dominant strategy.

b. Nash equilibrium is (Low, Low) with payoff (300, 250).

reason: Firm A has a dominant strategy. It will always opt Low no matter what Firm B chooses. So, in response, Firm B will choose Low too, as its payoff for Low (250) is higher than for High (100).

Hence (Low, Low) is the Nash equilibrium.