Question

Firms 1 and 2 are in the pizza business, but they face slightly different market conditions. Each firm faces the following demand for its product: Q₁=21-3P₁+2P₂ for firm 1, and Q₂=27-3P₂+2P₁ for firm 2. The cost to each firm of making a pizza is $5; it is constant. Firms can choose any price.

a. Find the solution to the Bertrand game (output, price, and profit for each firm).

b. Compare it to the cooperative solution.

c. Explain why this game is a Prisoner’s Dilemma.

Answer 1

(b)

For cooperative solution, the solution is similar to Cournot game. To obtain the solution, derive the inverse demand functions as follows:

The firms in Bertrand game are earning high profits by producing less output.
(c)

Prisoner’s dilemma refers to a situation in which each player(firm) adopts its dominant strategy when he could do better by cooperating with the other player(firm). Firms in a duopoly face prisoner’s dilemma because each firm charges a low price and earn low profits because if it charges a higher price, it will lose the market share to its rival.

In the Bertrand game , each firm, while trying to maximize its profits, assumes that the other firm's output is constant at the existing level. It is difficult to maintain cooperation in duopoly because it is not in the best interest of the individual firms. However, if firms cooperate with each other,the collective outcome would be improved and obtain high profits.