Each firm has a constant marginal cost and 0 fixed cost, but Firm 1 is more efficient. Specifically, Firm 1 has cost function C1(q1) = c1q1 and Firm 2 has cost function C2(q2) = c2q2, 0

(a) [6 points] Suppose the rule for splitting up demand when the prices are equal is that both firms equally divide and each gets half of the total demand. Is there a pure strategy Nash equilibrium of the game in which both firms charge the same price? If yes, please find all such pure strategy Nash equilibria. If no, please also write down your arguments.

1. [18 points] (Bertrand competition) Consider a variant of Bertrand's duopoly game. Two firms compete through price and the demand function is D(p) = x - P if p s a 0 if p > a Each firm has a constant marginal cost and O fixed cost, but Firm 1 is more efficient. Specifically, Firm 1 has cost function Ci(q1) = c191 and Firm 2 has cost function C2(q2) = C292, 0