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

Author

Listed:
  • Jason Shachat
  • J. Todd Swarthout
  • Lijia Wei

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," Experimental Economics Center Working Paper Series 2012-11, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University.
  • Handle: RePEc:exc:wpaper:2012-11
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    File URL: http://excen.gsu.edu/workingpapers/GSU_EXCEN_WP_2012-11.pdf
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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, Universitiy 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. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-966, June.
    4. 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.
    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, 2003. "Professionals Play Minimax," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 395-415.
    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 F. Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
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    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.
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    15. repec:spr:compst:v:59:y:2004:i:3:p:359-373 is not listed on IDEAS
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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 71878, University Library of Munich, Germany.

    More about this item

    Keywords

    Mixed Strategy; Nash Equilibrium; Experiment; Hidden Markov Model;

    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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