Question

Two firms are planning to sell 10 or 20 units of their goods and face the payoff matrix illustrated to the right. What is the Nash equilibrium if both firms make their decisions​ simultaneously? What strategy does each firm​ use? A. The game does not have a Nash equilibrium. B. The Nash equilibria are for Firm 1 to produce 10 and Firm 2 to produce 20 and for Firm 1 to produce 20 and Firm 2 to produce 10. C. The Nash equilibrium is for Firm 1 to produce 20 and Firm 2 to produce 10. D. The Nash equilibrium is for Firm 1 and Firm 2 each to produce 10. E. The Nash equilibrium is for Firm 1 to produce 10 and Firm 2 to produce 20

Answer 1

D. The Nash equilibrium is for Firm 1 and Firm 2 each to produce 10.

Step-by-step explanation:

Firm 2

10 units 20 units

10 units 30 / 50 /

Firm 1 30 35

20 units 40 / 20 /

60 20

(firm 1 /

firm 2)

Firm 1's dominant strategy would be to sell 10 units with an expected payoff outcome = 30 + 50 = 80

Firm 2's dominant strategy would be to sell 10 units with an expected payoff outcome = 30 + 60 = 90

Since both firms have the same dominant strategy (to produce 10 units), there is a Nash Equilibrium where both firms produce 10 units and each one earns 30.