Problem: The town of Utopia is popular to 2 popular diners, Joe's Diner and Ken's Diner. Both sell only fish pies. Everyone who considers eating at the 2 Diners is aware that they sell the same Fish Pies and knows the prices that they charge (P_J;P_K). At precisely 5:00pm, each diner simultaneously sets its price of fish pie for that evening. The market demand function for Fish Pie is Q = 120 - 20p where p is lower of the two diners prices. If there is a lower priced diner, then people eat fish pie at only that diner and the dinner sells 120 - 20p fish pies. If the two diners post the same price, then each sells to one half of the market: 1/2(120 - 20p). Suppose that prices can be quoted in dollars units only (0,1,2,3,4,5, or 6). Each diner's marginal cost is $2 and the fixed cost equal to zero

Required:

i) Create a 7*7 payoff matrix and fill in the diner's profits

ii) Identify all Nash Equilibria

iii) Suppose that Ken's Diner is out of business and Joe's is a monopoly. Find Joe's profit maximizing price.