Bachelor of Arts
Airlines, Travel, Game theory, Parable, Claims, Equilibrium
Game theory studies how people should respond in strategic situations and is naturally used for predictive purposes. The optimal strategy predictions yielded by game theoretic reasoning can be surprising when they conflict with preconceived notions of how to play, i.e. the "common sense" strategy. Consequently, the game theoretically optimal strategy may be a poor predictor of how individuals actually behave in real-life strategic situations. In order to accurately model such situations for predictive purposes it is important to know the limitations of the current game theoretic tools.
In the traveler's dilemma, Kaushik Basu presents a parable to illustrate how game theoretic reasoning and intuition can be at odds. The parable is as follows: Two travelers are returning home from a vacation where they purchased identical souvenirs. These souvenirs are, of course, routinely destroyed by the airline. The souvenirs were purchased with cash in an open-air market and as a result the travelers do not have receipts. The airline official in charge of damage claims wants to compensate the travelers fairly but has no way of determining the actual purchase price of the souvenirs. In an attempt to avoid spurious claims the official proposes a method to determine the amount awarded. Each traveler must submit a claim that lies between a known minimum and maximum. (The minimum bound can be thought of as that level of claim below which the airline never disputes for cost reasons and the maximum bound can be thought of as the most the airline's insurance company would pay absent a special policy). If the claims submitted are equal then both receive the amount claimed. However, if traveler 1 submits a lower claim than traveler 2, traveler 1 is considered "honest" and receives the lower claim plus a reward for honesty (ideally in frequent flyer miles thereby ensuring that the airline will have an opportunity to destroy those items which it missed on the first pass). Traveler 2 also receives the lower claim but in addition a symmetric penalty for "lying" is levied. Travelers report their claims simultaneously i.e., without knowledge of the other traveler's claim. This ensures that simple, collusive agreements cannot be reached because any such agreement involves a non-credible promise (the rewards are structured such that there it is never in a rational player's best interest to play as he agreed).
Game theoretic analysis suggests that two rational players will report the minimum claim. Moreover, this result is a direct consequence of both players attempting to maximize their individual payoff. Adoption of this strategy does not, on the face of it, appear to be the best strategy because both players can clearly improve their payoff simply by submitting random large claims.
Pelz, Eduard A., "An Analysis of the Traveler's Dilemma with Experimental Evidence" (1999). Honors Papers. 532.