Question

Consider a pizza pricing game, in which one store (Donna’s Deep Dish) is much larger than the other (Pierce’s Pizza Pies), and the stores have to decide whether to price High or Low. The payoff table for the game is:

Pierce's Pizza Pics High Low 132, 70 130, 50 Donna's High Deep Dish 156, 60

The noncooperative 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 sum of money. The alternative to this agreement is simply the noncooperative dominant-strategy equilibrium. They bargain over this agreement, and Donna’s has 3 times as much bargaining power as Pierce’s. In the resulting agreement, what sum will Donna’s pay to Pierce’s?

Answer 1

In the resulting agreement, the amount paid by Donna to Pierce is equal to 70 - 60 = $10 or the loss which Pierce has to bear if Donna forces Pierce to have cooperative agreement rather than non-cooperative dominant strategy equilibrium. Thus, Donna will pay to Pierce an amount equal to $10.