Suppose there are two firms in a market, a big incumbent firm (B) and a start-up challenger firm (C). They compete in a research and development (R&D) race with a random return M that is equally likely to be 0 or 1. There are two periods. R&D costs c > 0 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 move simultaneously, but decisions in the first period are observed before the second period. If one firm stays longer than the other, it gets M and the other 0. If both firms stay until the end, each firm gets . Otherwise, both get 0. There is no discounting of payoff between the two periods. A firm's payoff is the payoff at the end, minus the sum of R&D costs (if any). Firm B receives a noisy signal about M but Firm C does not. Prior to the decision in period 1, Firm B gets either good news, g, or bad news, b. The probability that the signal is g when M = 1 is q, where 2/3< q < 1. The probability that the signal is b when M = 1 is also q. Firm C is completely uniformed. Conditional on the signals, the expected returns are E[M|g] = q and the E[M|b] = 1 q. Good news makes Firm B optimistic while bad news makes it pessimistic. Suppose that the parameters satisfy (i) 2c <1>and (ii) c < 1 q < 2c.

(a) Formulate the situations above as a dynamic game with incomplete information. For the payoffs, you only need to describe those relevant for you to answer the next part.

(b) Is there a PBNE where the less informed firm, i.e., Firm C, always invests in the first period and obtains higher expected payoff than Firm B? If so, describe the PBNE and explain why this is a PBNE. If yes, but it requires one or more additional assumptions, state the assumption(s). If not, explain why.