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?
Cornell economist Kaushik Basu has a fascinating piece in the Scientific American on the game of traveller's dilemma. Not surprisingly, the way people answer the above question goes very strongly against the 'rational' solution. As Basu says:
[Traveller's dilemma] undermines both the libertarian idea that unrestrained selfishness is good for the economy and the game-theoretic tenet that people will be selfish and rational.
While on game theory, here's an earlier SciAm article -- The Economics of Fair Play (pdf) -- on Ultimatum and Public Goods games which show a strong evidence for people's sense of fair play, generosity and altruism. Charmingly irrational! The authors -- Karl Sigmund, Ernst Fehr and Martin Nowak -- combine these results with evolutionary psychology to conclude that "in social interactions, our preferences often turn out to be far from selfish.