Weblogsky: Traveler's Dilemma

« Face to Face | Main | Google sees FCC progress »

Traveler's Dilemma

I've been reading a Scientific American article on "The Traveler's Dilemma", and I really don't understand why it's such a quandary for the author, Kaushik Basu, and various researchers who've studied this scenario. Here's how it goes:

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.

According to the article, game theory assuming backward induction predicts that each player will select "2." Studies show that nobody makes the predicted choice, which is supposedly the most rational, and this seems to puzzle researchers. However it seems obvious to me: if I was playing the game, my selection of a number would be driven by an assumption that an antique would have a value greater than the very low end of the set of choices. In reading the scenario, I assumed that the actual value would be closer to the high end of the range presented. I wouldn't have imagined making a selection based solely on logic with no consideration of actual value. I find myself wondering why the researchers miss this? When I got to the paragraph that says "game theorists analyze games without all the trappings of the colorful narratives by studying each one's so-called payoff matrix...," I thought the article was going to be about real-world choices vs abstract predictive logic, but it really wasn't. The article's conclusion sort of acknowledges that there are paths to rational choice in this context:

If I were to play this game, I would say to myself: "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.

However, there's never any mention of actual value as a driver for the game-player's decision.

jon posted this at 9:19 AM
Share on Facebook| email to a friend