Consider a small town that has a population of dedicated pizza eaters but is able to accommodate only two pizza shops, Donna's Deep Dish and Pierce's Pizza Pies. Each seller has to choose a price for its pizza, but for simplicity, assume that only two prices are available: high and low. If a high price is set, the sellers can achieve a profit margin of $12 per pie; the low price yields a profit margin of $10 per pie. Each store has a loyal captive customer base that will buy $3000 pies per week, no matter what price is charged by either store. There is also a floating demand of $4000 pies per week. The people who buy these pies are price conscious and will go to the store with the lower price; if both stores charge the same price, this demand will be split equally between them.

(a)Draw the game table for the pizza-pricing game, using each store's profits per week (in thousands of dollars) as payoffs. Find the Nash equilibrium of this game and explain if it is a prisoner's dilemma or not and why.

(b)Now suppose that Donna's Deep Dish has a much larger loyal clientele that guarantees it the sale of $11'000 (rather than $3000) pies a week. Profit margins and the size of the floating demand remain the same. Draw the payoff table for this new version of the game and find the Nash equilibrium.

(c)How does the existence of the larger loyal clientele for Donna's Deep Dish help solve the pizza stores' dilemma?