Question

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 What is the Nash equilibrium for this game? A. Both firms producer low levels of output B. Firm A produces high levels of output, and Firm B produces low output. C. Both firms produce high levels of output D. Firm A produces low levels of output, and Firm B produces high output. E. There is more than one Nash equilibrium for this game

Answer 1

What is the Nash equilibrium for this game?

• A. Both firms produce low levels of output

Step-by-step explanation:

Nash equilibrium is achieved if both players' dominant strategies are the same:

Firm A

low output high output

low output 300 / 200 /

Firm B 250 75

high output 200 / 75 /

100 100

Firm A's dominant strategy = low output with an expected value of $300 + $200 = $500

Firm B's dominant strategy = low output with an expected value of $250 + $75 = $325

Since both firms' dominant strategies is to produce low outputs, then that is the Nash equilibrium.