Recall the variant of the pizza pricing game in Exercise U2, part (b), in Chapter 10, in which one store (Donna’s Deep Dish) was much larger than the other (Pierce’s Pizza Pies). The payoff table for that version of the game is: PIERCES PIZZA PIES
High Low
DONNAS
DEEP DISH High 156,60 132,70
Low 150,36 130,50
The non-cooperative dominant-strategy equilibrium is (High, Low), yielding profits of 132 to Donna’s and 70 to Pierce’s, for a total of 202. If the two could achieve (High, High), their total profit would be 156 + 60 = 216, but Pierce’s would not agree to this pricing.
Suppose the two stores can reach an enforceable agreement whereby both charge High and Donna’s pays Pierce’s a sum of money. The alternative to this agreement is simply the non-cooperative dominant-strategy equilibrium. They bargain over this agreement, and Donna’s has 2.5 times as much bargaining power as Pierce’s. In the resulting agreement, what sum will Donna’s pay to Pierce’s?