Question

Two firms have the option of setting the price of the their product at $10 or $20. Their profits are interdependent. This is the payoff matrix.

a. What is the Nash Equilibrium?

b. If these two firms decide to collude (work together), what prices will they choose?

Firm B P-$10 P-$20 P-$10 A profits $40, A profits $60, B profits $40 B profits $35 P-S20 A profits $35, | A profits $55, B profits $60 B profits $55 Firm A

Answer 1

a) Nash equilibrium is the point where none of the firm will deviate unilaterally or they will face a loss. Here, the Nash equilibrium is at price $10 and return 40. Starting form point where both of them are charging $20, the return is $55, but if the firm charge less the return for the firm will increase to $60, both will decease the price to $10.

b) If they collude they will charge $20 and the return will be $55 each.