An Experimental Study of the Centipede Game

Abstract

We report on an experiment in which individuals play a version of the centipede game. In this game, two players alternately get a chance to take the larger portion of a continually escalating pile of money. As soon as one person takes, the game ends with that player getting the larger portion of the pile, and the other player getting the smaller portion. If one views the experiment as a complete information game, all standard game theoretic equilibrium concepts predict the first mover should take the large pile on the first round. The experimental results show that this does not occur.An alternative explanation for the data can be given if we reconsider the game as a game of incomplete information in which there is some uncertainty over the payoff functions of the players. In particular, if the subjects believe there is some small likelihood that the opponent is an altruist, then in the equilibrium of this incomplete information game, players adopt mixed strategies in the early rounds of the experiment, with the probability of taking increasing as the pile gets larger. We investigate how well a version of this model explains the data observed in the centipede experiments.KEvwoRos: Game theory, experiments, rationality, altruism. OVERVIEW OF THE EXPERIMENT AND THE RESULTSTHIS PAPER REPORTS THE RESULTS of several experimental games for which the predictions of Nash equilibrium are widely acknowledged to be intuitively unsatisfactory. We explain the deviations from the standard predictions using an approach that combines recent developments in game theory with a parametric specification of the errors individuals might make. We construct a structural econometric model and estimate the extent to which the behavior is explainable by game-theoretic considerations.In the games we investigate, the use of backward induction and/or the elimination of dominated strategies leads to a unique Nash prediction, but there are clear benefits to the players if, for some reason, some players fail to behave in this fashion. Thus, we have intentionally chosen an environment in which we expect Nash equilibrium to perform at its worst. The best known example of a game in this class is the finitely repeated prisoners' dilemma. We focus on an even simpler and, we believe more compelling, example of such a game, the closely related alternating-move game that has come to be known as the "centipede game" (see Binmore (1987)).The centipede game is a finite move extensive form two person game in which each player alternately gets a turn to either terminate the game with a favorable payoff to itself, or continue the game, resulting in social gains for the pair. As 1 Support for this research was provided in part by NSF Grants #IST-8513679 and #SES-878650 to the California Institute of Technology. We thank Mahmoud El-Gama) for valuable discussions concerning the econometric estimation, and we thank Richard Boylan, Mark Fey, Arthur Lupia, and David Schmidt for able research assistance. We thank the JPL-Caltech joint computing project for granting...

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