A Bayesian Sequential Experimental Study of Learning in Games

Abstract

We apply a sequential Bayesian sampling procedure to study two models of learning in repeated games. In the first model individuals learn only about an opponent when they play her or him repeatedly but do not update from their experience with that opponent when they move on to play the same game with other opponents. We label this the nonsequential model. In the second model individuals use Bayesian updating to learn about population parameters from each of their opponents, as well as learning about the idiosyncrasies of that particular opponent. We call this the sequential model. We sequentially sample observations on the behavior of experimental subjects in the so-called “centipede game.” This game allows for a trade-off between competition and cooperation, which is of interest in many economic situations. At each point in time, the “state” of our dynamic problem consists of our beliefs about the two models and beliefs about the nuisance parameters of the two models. Our “choice” set is to sample or not to sample one more data point and, if we should not sample, which of the models to select. After 19 matches (4 subjects per match), we stop and reject the nonsequential model in favor of the sequential model.

Key Words:

• Bayesian learning
• Experimental design
• Game theory
• Preposterior analysis
• Sequential sampling