Suppose several friends go out to dinner with the understanding that thebill will be divided equally. The problem is that someone might ordersomething expensive, knowing that part of the cost will be paid by others.To analyze such a situation, suppose n diners are present, and, for sim- example, if three diners are present and each orders a different meal, thenplicity, they have the same food preferences. The accompanying tablestates the price of each of three dishes on the menu and how much eachthe payoff to the one ordering the pasta dish is(14 + 21 + 30`21 –= 21 – 21.67 = -0.67person values it. Value is measured by the maximum amount the personwould be willing to pay for the meal.the payoff for the person ordering the salmon isDining Dilemma14 + 21 + 30`26 –= 4.33DishValuePriceSurplus3Pasta Primavera$21.00$14.00$7.00and the payoff to whoever is ordering the steak isSalmon$26.00$21.00$5.0014 + 21 + 30`29 –= 7.33Filet Mignon$29.00$30.00-$1.003Not surprisingly, the people who order the more expensive meal do better,Surplus is just the value assigned to the meal, less the meal's price. The since all pay the same amount.pasta dish costs $14 and each diner assigns it a value of $21. Thus, if adiner had to pay for the entire meal, then each diner would buy the pastadish, since the surplus of $7 exceeds the surplus from either salmon orsteak. In fact, a diner would prefer to skip dinner then to pay the $30 forthe steak, as reflected by a negative surplus. A player's payoff equals thevalue of the meal she eats, less the amount she has to pay. The latter isassumed to equal the total bill divided by the number of diners. Fora. Suppose two diners are present (n = 2). What will they order (at aNash equilibrium)?b. Suppose four diners (n = 4) are present. What will they order (at aNash equilibrium)?

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Question

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, knowing that part of the cost will be paid by others.
To analyze such a situation, suppose n diners are present, and, for sim- example, if three diners are present and each orders a different meal, then
plicity, they have the same food preferences. The accompanying table
states the price of each of three dishes on the menu and how much each
the payoff to the one ordering the pasta dish is
(14 + 21 + 30`
21 –
= 21 – 21.67 = -0.67
person values it. Value is measured by the maximum amount the person
would be willing to pay for the meal.
the payoff for the person ordering the salmon is
Dining Dilemma
14 + 21 + 30`
26 –
= 4.33
Dish
Value
Price
Surplus
3
Pasta Primavera
$21.00
$14.00
$7.00
and the payoff to whoever is ordering the steak is
Salmon
$26.00
$21.00
$5.00
14 + 21 + 30`
29 –
= 7.33
Filet Mignon
$29.00
$30.00
-$1.00
3
Not surprisingly, the people who order the more expensive meal do better,
Surplus is just the value assigned to the meal, less the meal's price. The since all pay the same amount.
pasta dish costs $14 and each diner assigns it a value of $21. Thus, if a
diner had to pay for the entire meal, then each diner would buy the pasta
dish, since the surplus of $7 exceeds the surplus from either salmon or
steak. In fact, a diner would prefer to skip dinner then to pay the $30 for
the steak, as reflected by a negative surplus. A player's payoff equals the
value of the meal she eats, less the amount she has to pay. The latter is
assumed to equal the total bill divided by the number of diners. For
a. Suppose two diners are present (n = 2). What will they order (at a
Nash equilibrium)?
b. Suppose four diners (n = 4) are present. What will they order (at a
Nash equilibrium)?

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