Saturday, June 16, 2007

Traveler’s Dilemma

‘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?’

Kaushik Basu (a noted game theorist) has a non-technical and beautifully written exposition of this famous Traveler’s Dilemma problem in the most recent Scientific American. Real people who play such games do not behave rationally but, by so doing, derive a kind of meta-rationality since, as a consequence of not behaving rationally, they do much better than they would by behaving rationally. It is a paradox of rationality that also arises in standard Prisoner’s Dilemmas.

An entertaining and informative light read.

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