Suppose two identical firms are competing in Bertrand competition, so that they produce identical goods and compete by choosing prices p1 and p2. Consumer demand is:q=12-p

Since both firms produce identical goods, all consumers buy from whichever offers a lower price. If both firms select the same price, half of demand is purchased from each firm. Suppose these are software firms, so that marginal cost c = 0.

(a) In the Nash equilibrium, what is the price, quantity supplied, and profit of each firm?

(b) Suppose the firms are in a repeated game and discount the future at rate Show (with math!) that a Nash equilibrium is possible where firms collude and earn higher profits every period than in the one-shot game. Explain your reasoning.

(c) Suppose the two firms are colluding to earn higher profits. But now a third firm enters, which is in every way identical to the original two firms. However, now, collusion collapses and a price war ensues. How can this be? What does this tell us about the discount rate