Question

From problem 2 please answer and explain questions 1 , 2 and 3 thanks. Class Game Theory: topic, theory and illustrations.

Problem 2

An industry is currently monopolized by a single firm (the "incumbent" or firm 1). A second firm (the "challenger") is considering entry, which entails a positive cost F = $729 in addition to its production cost. If the challenger stays out, then its profit is zero, whereas if it enters, the firms simultaneously choose outputs (as in Cournot's model of duopoly). The cost to firm i  (i =1, 2) of producing qi units of output is 19qi. If the firms' total output is Q = q1 + q2, then the market price is P(Q) = 100 - Q.

1. Draw a game tree that represents this market competition.
2. Describe the players, player functions, terminal histories, and payoffs.
3. Determine the set of subgame perfect equilibria of the game. Explain clearly as possible.

Answer 1