Consider a quantity setting game with a potential entrant (E, player 1) and an incumbent (I, player 2). Market demand is:

p = 140 Q, where market quantity is the sum of the two firms quantities: Q = q_E + q_I . Both firms have constant marginal costs of 20. The game plays out this way:

The entrant decides whether to enter or not (play IN or OUT).

If E plays OUT, the incumbent plays as a monopolist, and chooses a quantity q_I . E gets the default payoff of zero, and I gets whatever profit corresponds to q_I .

If E plays IN, the two firms compete in a simultaneous move Cournot game. Payoffs are the profits based on q_E and q_I.

(a) Draw the extensive form for the game, including any information sets. How many subgames are there?

(b) What is the subgame perfect equilibrium? [Be careful about how you specify your strategies.] Also determine the equilibrium path, and equilibrium payoffs.

(c) Is there a Nash equilibrium (or several) of the game in which the entrant does not enter (E plays OUT at the first node)?