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A hidden Markov model for the detection of pure and mixed strategy play in games

Author

Listed:
  • Jason Shachat

    (Wang Yanan Institute for Studies in Economics and MOE Key Laboratory in Econometrics, Xiamen University)

  • J. Todd Swarthout

    (Department of Economics and Experimental Economics Center, Georgia State University)

  • Lijia Wei

    (Wang Yanan Institute for Studies in Economics and MOE Key Laboratory in Econometrics, Xiamen University)

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, and allows switching between these states. 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 non-stationary dynamics. We also explore the ability of the model to forecast action choice.

Suggested Citation

  • Jason Shachat & J. Todd Swarthout & Lijia Wei, 2012. "A hidden Markov model for the detection of pure and mixed strategy play in games," Working Papers 1202, Xiamen Unversity, The Wang Yanan Institute for Studies in Economics, Finance and Economics Experimental Laboratory, revised 07 Jul 2012.
    • Handle: RePEc:fee:wpaper:1202
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    References listed on IDEAS

    as
    1. Charles Noussair & Marc Willinger, 2011. "Mixed strategies in an unprofitable game: an experiment," Working Papers 11-19, LAMETA, Universtiy of Montpellier, revised Nov 2011.
    2. Bar-Eli, Michael & Azar, Ofer H. & Ritov, Ilana & Keidar-Levin, Yael & Schein, Galit, 2007. "Action bias among elite soccer goalkeepers: The case of penalty kicks," Journal of Economic Psychology, Elsevier, vol. 28(5), pages 606-621, October.
    3. Binmore, Ken & Swierzbinski, Joe & Proulx, Chris, 2001. "Does Minimax Work? An Experimental Study," Economic Journal, Royal Economic Society, vol. 111(473), pages 445-464, July.
    4. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-966, June.
    5. P.-A. Chiappori, 2002. "Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer," American Economic Review, American Economic Association, vol. 92(4), pages 1138-1151, September.
    6. Jason Shachat & J. Todd Swarthout, 2004. "Do we detect and exploit mixed strategy play by opponents?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 359-373, July.
    7. Ignacio Palacios-Huerta, 2001. "Professionals Play Minimax," Working Papers 2001-17, Brown University, Department of Economics.
    8. Robert W. Rosenthal & Jason Shachat & Mark Walker, 2003. "Hide and seek in Arizona," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 273-293, December.
    9. Morgan, John & Sefton, Martin, 2002. "An Experimental Investigation of Unprofitable Games," Games and Economic Behavior, Elsevier, vol. 40(1), pages 123-146, July.
    10. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    11. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
    12. Ochs Jack, 1995. "Games with Unique, Mixed Strategy Equilibria: An Experimental Study," Games and Economic Behavior, Elsevier, vol. 10(1), pages 202-217, July.
    13. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
    14. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 395-415.
    15. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, vol. 104(1), pages 189-226, May.
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    Cited by:

    1. Duffy, Sean & Naddeo, JJ & Owens, David & Smith, John, 2016. "Cognitive load and mixed strategies: On brains and minimax," MPRA Paper 89720, University Library of Munich, Germany.
    2. Knut Lehre Seip & Øyvind Grøn, 2016. "Leading the Game, Losing the Competition: Identifying Leaders and Followers in a Repeated Game," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-16, March.

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    More about this item

    Keywords

    Mixed Strategy; Nash Equilibrium; Experiment; Hidden Markov Model;
    All these keywords.

    JEL classification:

    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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