Games of strategy 4th ed ch 17

U1. Recall the variant of the pizza pricing game in Exercise U2, part (b), in Chapter 10, in which one store (Donnas Deep Dish) was much larger than the other (Pierces 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 noncooperative dominant-strategy equilibrium is (High, Low), yielding profits of 132 to Donnas and 70 to Pierces, for a total of 202. If the two could achieve (High, High), their total pro t would be 156 60 216, but Pierces would not agree to this pricing.

Suppose the two stores can reach an enforceable agreement whereby both charge High and Donnas pays Pierces a sum of money. The alter- native to this agreement is simply the noncooperative dominant-strategy equilibrium. They bargain over this agreement, and Donnas has 2.5 times as much bargaining power as Pierces. In the resulting agreement, what sum will Donnas pay to Pierces?