In this paper, we report the results of a series of experiments on a version of the centipede game in which the total payoff to the two players is constant. Standard backward-induction arguments lead to a unique Nash equilibrium outcome prediction, which is the same as the prediction made by theories of "fair" or "focal" outcomes. We find that subjects frequently fail to select the unique Nash outcome prediction. While this behavior was also observed in McKelvey and Palfrey (1992) in the "growing pie" version of the game they studied, the Nash outcome was not "fair", and there was the possibility of Pareto improvement by deviating from Nash play. Their findings could therefore be explained by small amounts of altruistic behavior. There are no Pareto improvements available in the constant-sum games we examine, hence explanations based on altruism cannot account for these new data. We examine and compare two classes of models to explain this data. The first class consists of non-equilibrium modifications of the standard "Always Take" model. The other class we investigate, the Quanta! Response Equilibrium model, describes an equilibrium in which subjects make mistakes in implementing their best replies and assume other players do so as well. One specification of this model fits the experimental data best, among the models we test, and is able to account for all the main features we observe in the data.

This research was supported in part by National Science Foundation grant #SES-9223701 to the California Institute of Technology. We thank Bob Forsythe and Ray Riezman for help in facilitating the use of the experimental laboratory at University of Iowa. We are grateful for comments and suggestions from participants at the 1993 ESA Fall Meetings, an editor, and an anonymous referee. Published as Fey, Mark, Richard D. McKelvey, and Thomas R. Palfrey. "An experimental study of constant-sum centipede games." International Journal of Game Theory 25, no. 3 (1996): 269-287.

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