A Bayesian Sequential Experimental Study of Learning in Games

We apply a sequential Bayesian sampling procedure to study two models of learning in repeated games. The first model is that individuals learn only about an opponent when they play her/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 non-sequential model. The second model is that 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 that the sequential model. We sequentially sample observations on the behavior of experimental subjects in the so called 'centipede game'. This game has the property of allowing 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 non-sequential model in favor of the sequential model