Unobserved Heterogeneity and Equilibrium : An Experimental Study of Bayesian and Adaptive Learning in Normal Form Games

We describe an experiment based on a repeated two-person game of incomplete information designed so that Jordan's Bayesian model of learning in games and the best response model make completely opposite predictions. Econometric analysis of the experimental data, using the maximum likelihood procedure introduced by El Gamal and Grether, reveals clear heterogeneity in the subjects' learning behavior. The heterogeneity is not diffuse, however: the subjects follow only a few decision rules for basing their play on their information, and the decision rules have simple cognitive interpretations. We show that the heterogeneity can be explained as an equilibrium of the repeated game. Although the repeated game has many equilibria, including a unique pure strategy equilibrium, we find that the only equilibrium consistent with the data is one of the mixed strategy equilibria. This equilibrium is shown, surprisingly, to be consistent with Jordan's Bayesian model, in a "representative player" sense, each subject using a pure strategy, but the distribution of strategies among subjects coinciding with the mixed strategy equilibrium