The Strategies Behind their Actions: A Method to Infer Repeated-Game Strategies and an Application to Buyer Behavior

We introduce a Bayesian method to infer repeated-game strategies in the form of ifthen statements that best describe individuals’ observed actions. We apply this method to buyer behavior in posted-offer market experiments. While the strategies of one-quarter of the buyers in our experiments correspond to the game-theoretic prediction of passive price-taking, for three-quarters of the buyers we infer repeated-game strategies that condition on time, price, and combinations of time and price. Our analysis fills a gap in a literature that studies the convergence of pricing behavior in posted-offer markets but has not addressed the market as a repeated game. We propose that strategy inference should at least complement existing methods of statistical inference on observed strategic behavior. keywords: strategy inference, repeated-game strategies, Bayesian methods, strategic buyer behavior, binary decision tree, experimental posted-offer market. JEL classification nos. C91, D42. Contact Information: Engle-Warnick: Department of Economics, 855 Sherbrooke St. W., McGill University, Montreal, QC, H3A 2T7, Canada, e-mail: [email protected], tel.: (514) 398-1559; fax: (514) 398-4938; Editorial communication should be sent to Ruffle at: Department of Economics, Ben-Gurion University, Beer Sheva, Israel, 84105, e-mail: [email protected], tel.: 972-8-6472308, fax: (917) 591-8151. Acknowledgements: We thank David Balan, John Duffy, Erik Eyster, Frank Gerhard, Margaret Meyer, Avi Weiss and seminar participants at the Economic Science Association meetings in Tucson and Amsterdam, and seminar participants in economics departments at Koc University, Lehigh University, McGill University, University of East Anglia, University College London, University of Oxford, Purdue University, Royal Holloway College, University of London, and University of Nottingham for valuable comments. We also thank Moty Fania for programming the posted-offer market software used to conduct the experiments. Engle-Warnick was supported in part by the University of Pittsburgh, Department of Economics through an Andrew W. Mellon fellowship. Ruffle thanks grants from the Russell Sage Foundation and Ben-Gurion University for funding.