Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-20T00:37:38.215Z Has data issue: false hasContentIssue false
  • English
  • Français

A HIDDEN MARKOV MODEL FOR THE DETECTION OF PURE AND MIXED STRATEGY PLAY IN GAMES

Published online by Cambridge University Press:  24 October 2014

Jason Shachat ,
J. Todd Swarthout  and
Lijia Wei
Jason Shachat
Affiliation:
Durham University
J. Todd Swarthout
Affiliation:
Georgia State University
Lijia Wei*
Affiliation:
Wuhan University
*
*Address Correspondence to Lijia Wei, School of Economics and Management, Wuhan University, China 430072; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose a statistical model to assess whether individuals strategically use mixed strategies in repeated games. We formulate a hidden Markov model in which the latent state space contains both pure and mixed strategies. We apply the model to data from an experiment in which human subjects repeatedly play a normal form game against a computer that always follows its part of the unique mixed strategy Nash equilibrium profile. Estimated results show significant mixed strategy play and nonstationary dynamics. We also explore the ability of the model to forecast action choice.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 4 , August 2015 , pp. 729 - 752
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The authors thank John Duffy, John Wooders, Jan Bouckaert, and Leonidas Spiliopoulos for discussion and comments on earlier drafts. We also thank the seminar participants at the University of Otago, Monash University, the University of Sydney, the Antwerp-Lille-Xiamen joint workshop in Microeconomics, and the 3rd WISE-Humboldt joint workshop on high-dimensional nonstationary econometrics. Jason Shachat acknowledges the Fujian Overseas High Talent Organization for funding as well as the NSF of China under proposal number 71131008.

References

REFERENCES

Ansari, A., Montoya, R., & Netzer, O. (2012) Dynamic learning in behavioral games: A hidden Markov mixture of experts approach. Quantitative Marketing and Economics 10, 475–503.CrossRefGoogle Scholar
Aumann, R.J. (1985) On the non-transferable utility value: A comment on the Roth-Shafer examples. Econometrica 53, 667–678.Google Scholar
Bareli, M., Azar, O., Ritov, I., Keidarlevin, Y., & Schein, G. (2007) Action bias among elite soccer goalkeepers: The case of penalty kicks. Journal of Economic Psychology 28, 606–621.CrossRefGoogle Scholar
Binmore, K., Swierzbinski, J., & Proulx, C. (2001) Does minimax work? An experimental study. Economic Journal 111, 445–464.CrossRefGoogle Scholar
Bloomfield, R. (1994) Learning a mixed strategy equilibrium in the laboratory. Journal of Economic Behavior & Organization 25, 411–436.Google Scholar
Camerer, C.F. & Ho, T.-H. (1999) Experience-weighted attraction in games. Econometrica 67, 827–874.Google Scholar
Chiappori, P., Levitt, S., & Groseclose, T. (2002) Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer. The American Economic Review 92, 1138–1151.CrossRefGoogle Scholar
Erev, I. & Roth, A.E. (1998) Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria. The American Economic Review 88, 848–881.Google Scholar
Geman, S. & Geman, D. (1987) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. In Fischler, M.A. & Firschein, O. (eds.), Readings in Computer Vision: Issues, Problems, Principles, and Paradigms, pp. 564–584. Morgan Kaufmann Publishers Inc.Google Scholar
Geweke, J. (1991) Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments. Staff Report 148, Federal Reserve Bank of Minneapolis.CrossRefGoogle Scholar
Greiner, B. (2004) An online recruitment system for economic experiments. In Kremer, K. & Macho, V. (eds.), Forschung und wissenschaftliches Rechnen, vol. 63 of Ges. fur Wiss. Datenverarbeitung, pp. 79–93. GWDG Bericht.Google Scholar
Nash, J. (1951) Non-cooperative games. Annals of Mathematics 54, 286–295.CrossRefGoogle Scholar
Noussair, C. & Willinger, M. (2011) Mixed Strategies in an Unprofitable Game: An Experiment. Working papers, LAMETA, University of Montpellier.Google Scholar
Nyarko, Y. & Schotter, A. (2002) An experimental study of belief learning using elicited beliefs. Econometrica 70, 971–1005.CrossRefGoogle Scholar
Ochs, J. (1995) Games with unique, mixed strategy equilibria: An experimental study. Games and Economic Behavior 10, 202–217.CrossRefGoogle Scholar
O’Neill, B. (1987) Nonmetric test of the minimax theory of two-person zero-sum games. Proceedings of the National Academy of Sciences of U.S.A. 84, 2106–2109.CrossRefGoogle Scholar
Palacios-Huerta, I. (2003) Professionals play minimax. Review of Economic Studies 70, 395–415.CrossRefGoogle Scholar
Rabiner, L.R. (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77, 257–286.CrossRefGoogle Scholar
Rosenthal, R.W., Shachat, J., & Walker, M. (2003) Hide and seek in Arizona. International Journal of Game Theory 32, 273–293.Google Scholar
Selten, R. & Chmura, T. (2008) Stationary concepts for experimental 2x2-games. The American Economic Review 98, 938–966.Google Scholar
Shachat, J. (2002) Mixed strategy play and the minimax hypothesis. Journal of Economic Theory 104, 189–226.CrossRefGoogle Scholar
Shachat, J. & Swarthout, J. Todd (2004) Do we detect and exploit mixed strategy play by opponents? Mathematical Methods of Operations Research 59, 359–373.CrossRefGoogle Scholar
Shachat, J. & Swarthout, J. Todd (2012) Learning about learning in games through experimental control of strategic interdependence. Journal of Economic Dynamics and Control 36, 383–402.Google Scholar
Shachat, J. & Wei, L. (2012) Procuring commodities: First-price sealed-bid or English auctions? Marketing Science 31, 317–333.Google Scholar
Von Neumann, J. (1928) Zur theorie der gesellschaftsspiele. Mathematische Annalen 100, 295–320.CrossRefGoogle Scholar
Von Neumann, J. & Morgenstern, O. (1944) Theory of Games and Economic Behavior. Princeton University Press.Google Scholar
Walker, M. & Wooders, J. (2001) Minimax play at Wimbledon. The American Economic Review 91, 1521–1538.CrossRefGoogle Scholar