Two companies are deciding at what point to enter a market. The market lasts for four periods and companies simultaneously decide whether to enter in period 1, 2, 3, or 4, or not enter at all. Thus, the strategy set of a company is {1,2,3,4,do not enter}. The market is growing over time, which is reflected in growing profit from being in the market. Assume that the profit received by a monopolist in period t (where a monopoly means that only one company has entered) is 10 x t - 15, whereas each duopolist (so both have entered) would earn 4 x t - 15. A company earns zero profit for any period that it is not in the market. For example, if company 1 entered in period 2 and company 2 entered in period 3, then company 1 earns zero profit in period 1; 5 ( = 10 x 2 - 15) in period 2; -3 ( = 4 x 3 - 15) in period 3; and 1 ( = 4 x 4 - 15) in period 4, for a total payoff of 3. Company 2 earns zero profit in periods 1 and 2, -3 in period 3, and 1 in period 4, for a total payoff of -2.
a. Derive the payoff matrix.
b. Derive a company’s best reply for each strategy of the other company.
c. Find the strategies that survive the IDSDS.
d. Find the Nash equilibria.