Consider the following two-stage game. At time 1, an incumbent firm (Firm 1) chooses its price (p1). At time 2, a potential entrant (Firm 2) decides whether to enter, and if so, chooses its price (p2). If Firm 2 enters, it must pay a fixed cost F<1/4. Market demand is given by Q=1-P, where P is equal to the minimum of p1 and p2. Assume that when both firms set the same price, all the demand goes to Firm 2. Assume all demand goes to the firm with the lower price when the firms' prices differ. The marginal cost of production for both firms is assumed to be zero.
1. Take p1 as given. Conditional on entering, what price will firm 2 set?
2. For what values of p1 will Firm 2 enter?
3. What price will Firm 1 choose at time 1?