The small town of Perkasie, PA, has two diners: Emil's Diner and Bobby Ray's Diner. Both sell only chicken pies. Everyone who would consider eating at the diners is aware that they sell the same chicken pies, and knows the prices that they charge (pE, pBR). At precisely 5 P.M., each diner (simultaneously) sets its price of chicken pie for that evening. The market demand function for chicken pie is Q= 100 - 20 p, 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 100 - 20 pchicken pies. If the two diners post the same price, then each sells to one-half of the market: ½(120 - 20 p). 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 fixed cost is $0.
a. Create a 7 × 7 payoff matrix, and fill in the matrix with the diners' profits.