Reference no: EM13191368

An incumbent in an industry faces the possibility of entry by a challenger. First the challenger chooses whether or not to enter. If it does not enter, neither firm has any further action; the incumbent's payoff is TM (it obtains the profit M in each of the following T = 1 periods) and the challenger's payoff is 0. If the challenger enters, it pays the entry cost f > 0, and in each of T periods the incumbent first commits to fight or cooperate with the challenger in that period, then the challenger chooses whether to stay in the industry or to exit. (Note that the order of the firms' moves within a period differs from that in the game in Example 152.1.) If, in any period, the challenger stays in, each firm obtains in that period the profit -F < 0 if the incumbent fights and C > max{F, f } if it cooperates. If, in any period, the challenger exits, both firms obtain the profit zero in that period (regardless of the incumbent's action); the incumbent obtains the profit M > 2C and the challenger the profit 0 in every subsequent period. Once the challenger exits, it cannot subsequently re-enter. Each firm cares about the sum of its profits.
a. Find the subgame perfect equilibria of the extensive game that models this situation.