Experts Playing the Traveler’s Dilemma

We analyze a one-shot experiment on the traveler’s dilemma in which members of the Game Theory Society, were asked to submit both a (possibly mixed) strategy and their belief concerning the average strategy of their opponents. Very few entrants expect and play the unique Nash equilibrium, while we observe a fifth playing the cooperative solution of the game, i. e. a strictly dominated strategy. The experimental data suggest to analyze the game as one of incomplete information. Most strategies observed are in the support of its Bayesian Nash equilibria. A notable exception is the Nash equilibrium strategy of the original game. (JEL C91, C72) The traveler’s dilemma was first described by Kaushik Basu (1994) at the conference of the American Economic Association in January 1994. Basu proposed this game in order to demonstrate the conflict between intuition and game-theoretic reasoning in a one-shot game. We report the results of an experiment conducted on this game as a one-shot game participants being experts in game theory, in particular members of the Game Theory Society. The parable for the traveler’s dilemma (Basu, 1994, pp. 391) is the following: “Two travelers returning home from a remote island, where they bought identical antiques [. . . ], discover that the airline has managed to smash these [. . . ]. The airline manager [. . . ] assures the passengers of adequate compensation. But since he does not know the cost of the antique, he offers the following scheme. Each of the two travelers has to write down on a piece of paper the cost of the antique. This can be any value between 2 units of money ∗This research started while Michael Carter was visiting the University of Hohenheim. Correspondence to Jörg Naeve, Economics Institute 520c, University of Hohenheim, 70593 Stuttgart, GERMANY; E-Mail: [email protected] Some month later, roughly the same game was presented in a philosophical journal under the title “The gingerbread game” (Martin Hollis, 1994).