The market is characterized by a demand function Q = 100-P and by a single firm with constant marginal cost c. The monopolist is facing potential entry from a new firm having the same marginal cost but an additional fixed cost of entry F = 10. If the incumbent accepts the entry, then Cournot competition is played. However, the monopolist can threaten to produce the competitive output (i.e., the quantity such that P = c) so that the new entrant will make losses if it enters the market. If the new firm does not enter, the incumbent behaves like a monopolist.

(a) Using the extensive form (game tree) representation, describe this entry game as a two-stage game where in the first stage the entrant decides whether to enter or not, and in the second stage, the incumbent firm decides whether to accommodate or fight in case of entry, while it does nothing in case the new firm does not enter the market.

(b) Is the threat of aggressive behavior by the monopolist credible? Answer the question by finding the subgame perfect equilibrium of the game.

(c) Describe the dynamic game using the normal form (pay-off matrix) representation and find the Nash equilibria of the game. Does the game have any Nash equilibria that are not subgame perfect?