Consider the following entry game we analyzed in class. There are two potential entrants (firm 1 and firm 2) that simultaneously decide whether or not to enter a market. If only one firm enters, the entering firm becomes a monopolist while the other firm that stays out gets zero profit. If both firms enter the market, they play a Cournot game. The demand in the market is given by P = 6Q. Assume that there is no production cost, but there is an entry cost of 5.

Do the problem above assuming that they play a Bertrand game if both firms enter the market.

a. What is the payoff of a firm that enters if the other firm stays out?

b. What is the payoff of a firm that enters if the other firm also enters?

c. Draw a 2 by 2 matrix of this entry game and derive all Nash equilibria (in pure and mixed strategies).