problem 5 (20 points) An industry is currently a monopoly and the incumbent monopolist is making a profit of $2 million. A potential entrant is considering whether or not to enter this industry. If she stays out, her profit will be $0 million; if she enters, the incumbent can either fight with a price war whose outcome is that each rm makes a loss of $1 million, or it can accommodate entry by sharing the market with the entrant, in which case each firm makes a profit of $1 million.

(a) Draw the extensive-form game associated with this situation.

(b) Describe the backward-induction equilibrium of this game.

(c) Write the strategic-form game associated with the situation.

(d) Describe and discuss the Nash equilibria of the strategic-form game in (c).