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.