The Traveler's Dilemma: When ‘Rational’ Isn’t ‘Optimal’

The last thing any airline passenger wants to hear is that the airline lost their luggage. But for our hypothetical traveler today, the headache is much bigger for three reasons: inside the suitcase are antiques, another passenger also lost a suitcase with an identical amount of antiques, and the airline established a series of strange conditions for the reimbursement. This brings us to the Traveler's Dilemma, in which two forces seek to obtain the maximum benefit, regardless of what happens to the other.

The game was originally presented in 1994 by Kaushik Basu, an Indian economist who served as Chief Economist of the World Bank between 2012 and 2016. It all begins with two travelers and an airline that loses their luggage.

Both suitcases are identical and have exactly the same content, which is composed of small antiques. Unsurprisingly, the passengers complain to the airline, and the manager in charge informs them that the company will reimburse up to a maximum of 100 dollars per suitcase.

The manager, unable to appraise the items, decides that to get the fairest and most balanced price, he needs to separate the travelers and block any possibility of them agreeing. Then he asks them to write down the value of their suitcase, with a minimum of 2 dollars and a maximum of 100.

If both write the same number, the manager and the company will take it as real and pay the sum without objections. But that is not all: If one of the numbers is smaller than the other, the company will take that value as the real one and pay that amount to both travelers, with an extra variable: The one who writes the smaller number will receive a bonus of two dollars, and the one responsible for the larger number will have a discount of two dollars.

The question is: What strategy should the travelers follow to determine the best value?

The Traveler's Dilemma: Breaking the Equilibrium

This is where the Traveler's Dilemma melts brains, because at the end of the chain… the value is two dollars. Why? Because those two dollars are the so-called Nash Equilibrium. The first thing that comes to mind is that they should cut their losses and claim 100 dollars.

If both passengers write the same number, they get that money and that’s it. But if we take into account the conditions established by the game, those 100 dollars do not represent the maximum benefit.

If the first traveler writes 99 dollars and the second writes 100, the first traveler will end up with 101 dollars in hand. Now, if the second traveler manages to detect this, he can turn the situation in his favor by writing 98. And the first writes 97. And the second writes 96. And the first writes 95… I think you get the idea. The cycle of analysis and counter-offer continues until reaching the Nash Equilibrium, which are those miserable two dollars.

In essence, following the Nash Equilibrium makes the manager end up on the floor laughing, because the company will pay a fraction of the original value of the suitcases.

However, in experimental evaluations, the majority of participants moved far away from the Nash Equilibrium, obtaining rewards closer to the 100 dollars. The Traveler's Dilemma proves that under certain conditions, rational strategies fly out the window, and the player tries to adopt optimal strategies.

In other words, sometimes it is rational to make an irrational decision. On the other hand, when the game is analyzed in groups, the results tend to be more rational and closer to the Nash Equilibrium.