Fictitious Play: A Statistical Study of Multiple Economic Experiments

Abstract

This paper illustrates the use of a full Bayesian procedure to update an experimenter's belief over various economic behavioral hypotheses using data from a variety of (potentially very different) experiments. Our example uses experimental data to update our belief as to whether individuals select strategies according to fictitious play. We endow the experimenter with priors over the events that players act according to fictitious play and according to the Cournot process. We then numerically compute the likelihood function for each experiment by replicating the experimental design and running the experiment with robots that behave according to each of our hypotheses. Updating experiment by experiment shows that some of the experiments favor Cournot, but most of them favor fictitious play as the more likely hypothesis. This illustrates the limitations of a classical procedure that can take only one experiment into consideration since some of the experiments may be misleading. Indeed, when we did the overall updating using 9 experiments, we found that, for any priors, the overall posterior put probability very close to one on the individuals acting according to fictitious play. Given the heterogeneity in the payoffs and design of the experiments that we combine for that overall posterior, it is clear that there is no classical procedure that would offer the same type of information.

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