Three firms, A, B and C engage in Bertrand price competition in a market with inverse demand given by P = 123 − 2Q. Whenever a firm undercuts the rivals’ price, it gets the entire demand. If firms charge the same lowest price in the market, they share the market. If a firm charges a price more than any rival, it has zero market share. Suppose there are no fixed costs, and the marginal costs of the firms are: c(A) = 91, c(B) = 83 and c(C) = 43. a. Find a Nash equilibrium of this game. What are each firm’s prices and profits? Explain your solution. b. Suppose firm B leaves the market. Draw each firm’s best response on a diagram and find a Nash equilibrium of this duopoly game. c. Suppose the above game in part b between firms A and C was the stage game of an infinitely repeated game. Would it be possible for the two firms to collude or form a cartel in this case?
Three firms, A, B and C engage in Bertrand price competition in a market with inverse demand given by P = 123 − 2Q. Whenever a firm undercuts the rivals’ price, it gets the entire demand. If firms charge the same lowest price in the market, they share the market. If a firm charges a price more than any rival, it has zero market share. Suppose there are no fixed costs, and the marginal costs of the firms are: c(A) = 91, c(B) = 83 and c(C) = 43. a. Find a Nash equilibrium of this game. What are each firm’s prices and profits? Explain your solution. b. Suppose firm B leaves the market. Draw each firm’s best response on a diagram and find a Nash equilibrium of this duopoly game. c. Suppose the above game in part b between firms A and C was the stage game of an infinitely repeated game. Would it be possible for the two firms to collude or form a cartel in this case?
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