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September 21, 2007
Competitive valuation problem
Lucy and Pete, returning from a remote Pacific island, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it.Instead he devises a more complicated scheme. He asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty--the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Lucy writes 46 and Pete writes 100, Lucy will get $48 and Pete will get $44.
What numbers will Lucy and Pete write? What number would you write?
The Scientific American examines this game with the tools of game theory and experimental economics in The Traveler's Dilemma. I enjoyed it, although from the sums involved, I question the implications of that result. When these games have minimum and maximum outcomes that are small relative to average income, the cooperative outcomes provide a kind of psychic benefit ("feel good") that is large relative to the size of the prizes. This has got to pollute the result. Combine this with the analytic difficulty of solving these recursive games, and these empirical results seem natural.
However, imagine that the prizes are in millions (from $2,000,000 to $100,000,000) and participants with proper quantitative and analytic training. Do you think the results would be the same? I think not.
Posted by OneEyedMan at September 21, 2007 8:12 AM
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