Question 3 (6 marks) Firm A is currently a monopolist in the market and the monopoly prots are $20, 000. At t = 1 Firm B decides whether to invest :2: dollars and enter the market, or not incur any investment costs and stay out of the market. If Firm B decides to stay out, Firm A remains a monopolist, and Firm B holds on to the full value of the investment. If Firm B decides to enter, then Firm A moves and decides whether to cooperate with Firm B and produce the Cournot quantity, or ght Firm B and produce more than the Cournot output which would drive prices and prots down. If Firm A cooperates, Firm A makes half of the monopoly prots, and Firm B makes half of monopoly prots less investment costs. If Firm A ghts, Firm B makes $5, 000 less investment costs, and Firm A makes $5, 000. a) Use a game tree to formulate the above situation as a game of sequential moves. (1 mark} b) Suppose that at the beginning of the game Firm A announces to Firm B \"If you enter, I will ght". Are there any values of :2: for which this announcement is a credible threat? Explain your answer. ('1 mark) c) Let .r: = $4, 000. Write the game tree and nd all subgame-perfect Nash equilibria (SPNE). {I mark) d) For what values of :2: would Firm B decide to enter the market? For what values of :2: would Firm B decide to stay out of the market? Explain your answers. (I mark} e) Let :2: = $4, 000 and assume that the two rms announce their actions simultaneously. Write the matrix of this static game and nd all Nash equilibria in pure strategies. {1 mark) Is there a Nash equilibrium that is based on a non-credible threat? Explain your answer. {I mark)