Three firms, A, B and C engage in Bertrand price competition in a market with inverse demand given by P = 10 Q.

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) = 8, c(B) = 6 and c(C) = 4.

a. FindaNashequilibriumofthisgame.Whatareeachfirm'spricesand profits? Explain your solution.

b. SupposefirmBleavesthemarket.Draweachfirm'sbestresponseonadiagram and find a Nash equilibrium of this duopoly game.