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?
The payoff matrix:
|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.
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