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

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  • Shachat, Jason
  • Swarthout, J. Todd
  • Wei, Lijia

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

  • Shachat, Jason & Swarthout, J. Todd & Wei, Lijia, 2012. "A hidden Markov model for the detection of pure and mixed strategy play in games," MPRA Paper 39896, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:39896
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    References listed on IDEAS

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    3. 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.
    4. Morgan, John & Sefton, Martin, 2002. "An Experimental Investigation of Unprofitable Games," Games and Economic Behavior, Elsevier, vol. 40(1), pages 123-146, July.
    5. 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.
    6. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    7. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, vol. 104(1), pages 189-226, May.
    8. Charles Noussair & Marc Willinger, 2011. "Mixed strategies in an unprofitable game: an experiment," Working Papers 11-19, LAMETA, Universtiy of Montpellier, revised Nov 2011.
    9. 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.
    10. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-966, June.
    11. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 395-415.
    12. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
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    Cited by:

    1. Sean Duffy & J. J. Naddeo & David Owens & John Smith, 2024. "Cognitive Load and Mixed Strategies: On Brains and Minimax," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 1-34, September.
    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; 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
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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