Question 4 [31! marks] Suppose there are two firms in a market. a big incumbent firm {Bi and a start-up challenger rm (6}. They compete in a research and development [asp] race with a random return M that is equally likely to be ill or 1. There are two periods. can costs c :2: l] per period. In the first period, a firm decides whether or not to enter the race by investing. If the firm does invest. in the second period. it decides whether or not to invest again. In each period, firms moye simultaneoust but decisions in the rst period are observed before the second period. If one rm stays longer than the other. it gets M and the other D. If both rms stay until the and. each rm gets %. theryse. both get i]. There is no discounting of payoff between the two periods. A firm's payoff is the payoff at the and. minus the sum of Fla-D costs [if any). Firm B receives a noisy signal about M but Firm C: does not. Prior to the decision in period 1. rm B gets either good news. 9. or bad news. a. The probability that the signal is p when M = 1 is q. where '3' a: q r: 1. The probability that the signal is i: when M = 1 is also g. Firm f: is completely uniformed. Conditional on the signals. the expected returns are E[M|g] = q and the E[M|E:] = 1 q. Good news makes FlrlTl B optimistic while bad news makes it pessimistic. Suppose that the parameters satisfy iii 2s a: g jq; and {ii} :1: a: 1 g a: 2c. la} Formulate the situations aboye as a dynamic game with incomplete information. For the payoffs. you only need to describe those relevant for you to answer the next part. {15 marks] lb} Is there a PBNE where the less informed rm, i.e.. Firm G. always invests in the rst period and obtains higher expected payoff than Firm B? If so, describe the F'BNE and explain why this is a FBNE. If yes. but it requires one or more additional assumptions. state the assumption{s}. If not. explain why. {15 marks}