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Published August 31, 2017 | Submitted
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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.

Additional Information

Revised version. Original dated to February 1991. We acknowledge the financial support from NSF grant #SES-9011828 to the California Institute of Technology. We also acknowledge the able research assistance of Mark Fey, Lynell Jackson and Jeffrey Prisbrey in setting up the experiments, recruiting subjects and running the experiments. We acknowledge the help of the Jet Propulsion Laboratory and its staff members for giving us access to their Cray XMP/18, and subsequently their Cray YMP2E/116. We thank Gary Lorden for a valuable discussion. We also thank, without implicating, two editors and one associate editor of JASA and three referees for their very careful and useful comments on earlier versions. Published as El-Gamal, Mahmoud A., Richard D. McKelvey, and Thomas R. Palfrey. "A Bayesian sequential experimental study of learning in games." Journal of the American Statistical Association 88, no. 422 (1993): 428-435.

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