10 diners meet for dinner. They agree beforehand that they will split the bill a
ID: 3271333 • Letter: 1
Question
10 diners meet for dinner. They agree beforehand that they will split the bill among them, i.e., every diner will pay 1/10 of the total bill. The restaurant has two dishes, chili crab and fish head curry. Everyone agrees that the chili crab is superior to the fish head curry. To quantify this we say that the chili crab is worth 30$, while the fish head curry is worth 20$. Outrageously, the chili crab is priced at 100$, while the fish head curry comes at 20$. Every diner will order one of the dishes for themselves (dishes are one portion only) and they do not share food. The diners are rational, and this is common knowledge. Show that ordering the chili crab strictly dominates ordering the fish head curry. The payoff of a diner is the value of the dish ordered minus the price paid (total bill divided by 10).Explanation / Answer
Price of the chili crab = 100$
Price of the fish head curry = 20$
Share of each person = 1/10
See the table below for various combinations of orders
From the last two columns above we see the net loss/profit incurred if chili crab is ordered or fish head curry is ordered. Ordering chili crab always gives non-negative net while ordering the fish head curry gives non-positive net.
Clearly ordering the chili crab strictly dominates ordering the fish curry.
Chili crab Fish head curry Cost (in dollars) Person share Net for chili crab Net for fish head curry 10 0 1000 100 0 -80 9 1 920 92 8 -72 8 2 840 84 16 -64 7 3 760 76 24 -56 6 4 680 68 32 -48 5 5 600 60 40 -40 4 6 520 52 48 -32 3 7 440 44 56 -24 2 8 360 36 64 -16 1 9 280 28 72 -8 0 10 200 20 80 0Related Questions
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