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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...

The paradox of not voting is examined in a model where voters have uncertainty about the preferences and costs of other voters. In game-theoretic models of voter participation under complete information, equilibrium outcomes can have substantial turnout even when voting costs are relatively high. In contrast, when uncertainty about preferences and costs is present, only voters with negligible or negative net voting costs participate when the electorate is large.

I t is widely believed that rational choice theory is grossly inconsistent with empirical observations about voter turnout. We report the results of an experiment designed to test the voter turnout predictions of the rational choice Palfrey-Rosenthal model of participation with asymmetric information. We find that the three main comparative statics predictions are observed in the data: the size effect, whereby turnout goes down in larger electorates; the competition effect, whereby turnout is higher in elections that are expected to be close; and the underdog effect, whereby voters supporting the less popular alternative have higher turnout rates. We also compare the quantitative magnitudes of turnout to the predictions of Nash equilibrium. We find that there is undervoting for small electorates and overvoting for large electorates, relative to Nash equilibrium. These deviations from Nash equilibrium are consistent with the logit version of Quantal Response Equilibrium, which provides a good fit to the data, and can also account for significant voter turnout in very large elections.

This paper investigates the use of standard econometric models for quantal choice to study equilibria of extensive form games. Players make choices based on a quantal choice model, and assume other players do so as well. We define an Agent Quantal Response Equilibrium (AQRE), which applies QRE to the agent normal form of an extensive form game and imposes a statistical version of sequential rationality. We also define a parametric specification, called logit-AQRE, in which quantal choice probabilities are given by logit response functions.AQRE makes predictions that contradict the invariance principle in sys tematic ways. We show that these predictions match up with some exper imental findings by Schotter, Weigelt and Wilson (1993) about the play of games that differ only with lcspect to inessential transformations of the ex tensive form. The logit-AQRE also implies a unique selection from the set of subgame perfect equilibria in generic extensive form games. We examine data from signalling game experiments by Banks, Camerer, and Porter (1994) and Brandts and Holt (1993) . We find that the logit-AQRE selection applied to these games succeeds in predicting patterns of behavior observed in these ex periments, even when our prediction conflicts with more standard equilibrium refinements, such as the intuitive criterion. We also reexamine data from the McKelvey and Palfrey (1992) centipede experiment.