4. Consider a dynamic two-stage game of complete and imperfect information between two firms. Firm 1 is a potential entrant and firm 2 is an incumbent. In the first state, firm 1 decides whether to enter the market (E) or to stay out (O). If firm 1 stays out, the game ends, firm 1 gets a payoff of zero and firm 2 gets a payoff of 10. If firm 1 enters the market, then in the second stage of the game firms 1 and 2 simultaneously and independently choose between A and B (you can think of A and B as alternative strategic plans involving several dimensions: pricing, advertising, product differentiation, etc.). The payoffs of the second stage interaction are described in the following payoff matrix , Firm 2 A B Firm 1 A -4, -4 1, 2 B 2, 1 -2, -2 (a) Represent the game in extensive form (game tree). (b) Represent the game in strategic form (matrix). Find all pure-strategy NE in the game. Remember to indicate Nash equilibria by the their corresponding strategy profiles (not payoffs). (c) Find all pure-strategy SPNE in the game. Remember to indicate SPNE by the their corresponding strategy profiles (not payoffs). (d) Find a SPNE in which players play mixed-strategies in the proper subgame