An experimental study of constant-sum centipede games

In this paper, the authors 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. The authors find that subjects frequently fail to select the unique Hash outcome prediction. While this behavior was also observed in McKelvey and Palfrey 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 the authors examine. Hence, explanations based on altruism cannot account for these new data. They examine and compare two classes of models to explain these data. The first class consists of non-equilibrium modifications of the standard ‘Always Take’ model. The other class the authors investigate, the Quantal 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 model, they test, and is able to account for all the main features the authors observe in the data.