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?
Traveler’s Dilemma (TD) achieves those goals because the game’s logic dictates that 2 is the best option, yet most people pick 100 or a number close to 100–both those who have not thought through the logic and those who fully understand that they are deviating markedly from the “rational choice. Furthermore, players reap a greater reward by not adhering to reason in this way. Thus, there is something rational about choosing not to be rational when playing Traveler’s Dilemma.
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In summary the article says: “Forget game-theoretic logic. I will play a large number (perhaps 95), and I know my opponent will play something similar and both of us will ignore the rational argument that the next smaller number would be better than whatever number we choose. What is interesting is that this rejection of formal rationality and logic has a kind of meta-rationality attached to it. If both players follow this meta-rational course, both will do well. The idea of behavior generated by rationally rejecting rational behavior is a hard one to formalize. But in it lies the step that will have to be taken in the future to solve the paradoxes of rationality that plague game theory and are codified in Traveler’s Dilemma.”
