The town of Perkasie, Pennsylvania, has two diners: Emil’s Diner and Bobby Ray’s Diner. Both sell only chicken pies. Everyone who considers eating at the diners is aware that they sell the same chicken pies and knows the prices that they charge At precisely 5:00 P.M., each diner (simultaneously) sets its price of chicken pie for that evening. The market demand function for chicken pie is , where p is the lower of the two diners’ prices. If there is a lower-priced diner, then people eat chicken pie at only that diner and the diner sells  chicken pies. If the two diners post the same price, then each sells to one-half of the market:  Suppose that prices can be quoted in dollar units only (0, 1, 2, 3, 4, 5, or 6). Each diner’s marginal cost is $2 and the fixed cost is $0.

a. Create a payoff matrix and fill in the diners’ profits.

b. Identify all Nash equilibria.

c. Suppose that Bobby Ray’s Diner is out of business and that Emil’s is a monopoly. Find Emil’s profitmaximizing price.

d. Now return to the Emil’s-versus-Bobby Ray’s game. Pick one of the Nash equilibria that you identified in part b. Could the two diners collude—set prices different from the particular Nash equilibrium prices and increase both diners’ profits? V