Game Theory

4. A small city has only two decent restaurants. Chez Ordinaire and Bistrot de Luxe. Each of these restaurants offers 3 grades of dinner, a light plate, a house special, and the grand dinner. The prices of the three types of dinners in Chez Ordinaire are shown in the third column of the table below. The value that each member of a group of acquaintances in this city places on each of these meals is given in the second column.

Table 3: Meals at Chez Ordinaire

	Value	Price
Light Plate	15	10
House Special	25	15
Grand Dinner	35	40

All of these people agree that Bistrot de Luxe has better food, but it costs more. Bistrot de Luxe also serves three grades of meals. Their costs and values to this group of friends are shown in the following table. The payoff to any of these individuals who eats at either of the restaurants is the value of the meal that he or she eats minus the amount of money that he or she has to pay for a meal

Table 4: Meals at Bistrot de Luxe

	Value	Price
Light Plate	30	20
House Special	50	60
Grand Dinner	70	80

A) If one of these people eats alone and pays for her own meal which restaurant should she go to and what should she order to maximize her payoff?

B) Suppose two people go out to eat together and they agree to split the check equally. Each chooses his or her dinner item separately. If they go to Chez Ordinaire, then in Nash equilibrium, what will each of them order? If they go to Bistrot De Luxe, what will each of them order? Explain

C) Suppose four people go out to eat together and they agree to split the check equally. Each chooses his or her dinner item separately. If they go to Chez Ordinaire, then in Nash equilibrium, what will each of them order? If they go to Bistrot De Luxe, what will each of them order? Explain

D) Suppose that two people are going out to dinner. They both know that they will split the check equally, and that, whichever restaurant they go to, the outcome will be a Nash equilibrium. Which restaurant will they choose? Explain.

E) Suppose that four people are going out to dinner. They plan to split the check equally, and they know that, whichever restaurant they go to, the outcome will be a Nash equilibrium. Which restaurant will they choose? Explain