Consider a variant version of the Bertrand model we learned in class. Two firms

compete through price and the demand function is D(p) = 100 p when p < 100

and 0 when p 100. 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) = 10q1

and Firm 2 has cost function C2(q2) = 20q2. Suppose that the price chosen by

each firm can only be an integer. Find all the Nash equilibria of the game.