Suppose several friends go out to dinner with the understanding that the bill will be divided equally. The problem is that someone might order something expensive, know- ing that part of the cost will be paid by others. To analyze such a situation, suppose n diners are present, and, for simplicity, they have the same food preferences. The accompanying table states the price of each of three dishes on the menu and how much each person values it. Value is measured by the maximum amount the person would be willing to pay for the meal.

Dining Dilemma Dish Value Price Surplus Pasta Primavera $21.00 $14.00 $7.00 Salmon $26.00 $21.00 $5.00 Filet Mignon $29.00 $30.00 -$1.00