http://www.sciam.com/article.cfm?chanID=sa006&articleID=7750A576-

E7F2-99DF-3824E0B1C2540D47&ref=rss

The link above leads to a very well known game, much like the Prisoner’s Dilemma, created by Cornell University professor Kaushik Basu. The problem is as follows: Two people are returning home from vacation on a plane and both have brought back with them an identical souvenir. Upon arriving at the airport after their trip, they both discovery that each of their souvenirs were damaged. The airlines is willing to compensate each of them for the loss, however, it does not know how much the souvenir costs, and for the sake of argument, each traveler did not save a receipt. So, the airlines decides to compensate them as follows, it asks both travelers to write down the amount they paid for the item but without talking to one another. If they both write the same amount, then the airlines will believe them and compensate them with that amount. If they write differing amounts, then the airlines will assume that the person who wrote the higher price is lying and trying to scam more money away from the company, so they will pay each traveler the lower amount. However, they will also give a bonus to the “truthful” traveler and pay him an extra $2 for not lying and take away $2 from the traveler who lied and wrote the larger amount. Here’s an example, is Traveler 1 writes down $60 and Traveler 2 writes down $100, then Traveler 1 gets $62 and Traveler 2 gets $58. The question is, what amount would you write if you were one of the travelers?

This problem has been experimented with many people and many answers have been given. When giving the actual value of the item, many write down that value, when told to write an answer between $2 and $100 many write a number in the $90s range. However, the intriguing part about this question, and what makes it a dilemma, is that the answer goes against rationality to some degree. The answer that game theory analysis gives us is $2, that is to say, if you were one of the travelers, you should write $2. We come up with this answer through a sort of backward induction. For example, if you were told to write a number between 2 and 100, many would assume that the other traveler would write 100 and therefore you should as well so that you both receive $100. However, if you believe this, then you should deviate to write down 99 so that you would receive $101 and the other traveler would receive $97. But, because of common knowledge, the other traveler knows you know this so he will write 99 as well and both of you will receive $99. Then again, from here, if you deviate to 98 then you will receive $100 dollars. This backward argument can be made for both all the way down until both players reach $2. This is what makes it odd, that game theory states the answer should be $2, however, no one would write down $2, if they were truly “rational.”

This problem is another example to one we learned in class where the “game theory” answer doesn’t always lead to a socially optimal solution as in the Prisoner’s Dilemma. In the PD, both should confess, however, if both would have not confessed then they both would have been better off. The Traveler’s Dilemma is a great game and if you want to learn a lot more about it, I encourage you all to read more about it in the article linked above!