Suppose N1 number of friends go out to dinner with the understanding that the total bill will be divided equally. For simplicity, assume that there are 4 diners (N=4). Also, assume that there are only three dishes on the menu, and they place their orders simultaneously. Not placing an order is not an option. The accompanying table states the price of each of the 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 dish. Surplus is the value assigned to the dish, less the dish's price. Each diner's objective is to maximize his/her surplus.

Dish Value Price

Filet Mignon $20.00 $10.00

Salmon $40.00 $48.00

Hamburger $44.00 $80.00

1. Find out a Nash equilibrium. Please justify your answer.
2. What will each of them order at the Nash equilibrium derived in part (1) above?
3. What would each of them order if he/she were alone?
4. In this problem, does each person order the same dish irrespective of whether he/she is alone or in the group? If not, then justify your answer.
5. Is it possible to have more than one Nash equilibrium in this problem? If yes, find out another Nash equilibrium. If not, justify your answer.
6. How would your answers to parts (1) & (2) change as N gets larger? Justify your answer.