Question

Consider the following game: Two firms simultaneously decide whether or not to enter a market. Each firm must pay a fixed entry cost of c if it decides to enter. After making their entry decisions, each firm observes whether or not its rival entered, and then chooses a production level. If both firms enter, production levels are chosen simultaneously. Market demand is given by p(q) = 8 − Q, where Q is the total market production. If a firm enters the market, it can produce at a marginal cost of 2. If a firm does not enter the market, it makes zero profits. 1. Suppose first that c = 2. If one firm enters and its rival does not, what are the entrant’s profits? (a) 7 (b) 9 (c) 5 (d) 3 2. Still assuming that c = 2, if both firms enter, what are each firm’s profits? 1 (a) 6 (b) 2 (c) 8 (d) 4 3. Again, if c = 2, what quantity will each firm produce in the Subgame Perfect Nash Equilibrium of this game? (a) 2 (b) 6 (c) 4 (d) 0 4. Suppose instead that c = 5. What is the equilibrium price in any pure strategy Subgame Perfect Nash Equilibrium of this game? By a pure strategy SPNE, I mean an equilibrium in which none of the firms plays a mixed strategy in any subgame of the game. (a) 6 (b) 5 (c) 7 (d) 4

Answer 1