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

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  • 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.

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File URL: http://feel.xmu.edu.cn/RePEc/wpaper/A_hidden_Markov_model_for_the_detection_of_pure_and_mixed_strategy_play_in_games.pdf
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Bibliographic Info

Paper provided by Xiamen Unversity, The Wang Yanan Institute for Studies in Economics, Finance and Economics Experimental Laboratory in its series Working Papers with number 1202.

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Length: 26 pages
Date of creation: 07 Jul 2012
Date of revision: 07 Jul 2012
Handle: RePEc:fee:wpaper:1202

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

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  1. Jason Shachat & J. Todd Swarthout, 2004. "Do we detect and exploit mixed strategy play by opponents?," Computational Statistics, Springer, Springer, vol. 59(3), pages 359-373, 07.
  2. Charles Noussair & Marc Willinger, 2011. "Mixed strategies in an unprofitable game: an experiment," Working Papers, LAMETA, Universtiy of Montpellier 11-19, LAMETA, Universtiy of Montpellier, revised Nov 2011.
  3. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, American Economic Association, vol. 98(3), pages 938-66, June.
  4. Bar-Eli, Michael & Azar, Ofer H. & Ritov, Ilana & Keidar-Levin, Yael & Schein, Galit, 2005. "Action bias among elite soccer goalkeepers: The case of penalty kicks," MPRA Paper 4477, University Library of Munich, Germany.
  5. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 70(2), pages 395-415, 04.
  6. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, Elsevier, vol. 104(1), pages 189-226, May.
  7. Robert W. Rosenthal & Jason Shachat & Mark Walker, 2003. "Hide and seek in Arizona," International Journal of Game Theory, Springer, Springer, vol. 32(2), pages 273-293, December.
  8. Ochs Jack, 1995. "Games with Unique, Mixed Strategy Equilibria: An Experimental Study," Games and Economic Behavior, Elsevier, Elsevier, vol. 10(1), pages 202-217, July.
  9. Binmore, Ken & Swierzbinski, Joe & Proulx, Chris, 2001. "Does Minimax Work? An Experimental Study," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 111(473), pages 445-64, July.
  10. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
  11. 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, American Economic Association, vol. 92(4), pages 1138-1151, September.
  12. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report, Federal Reserve Bank of Minneapolis 148, Federal Reserve Bank of Minneapolis.
  13. Morgan, John & Sefton, Martin, 2002. "An Experimental Investigation of Unprofitable Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 40(1), pages 123-146, July.
  14. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, Econometric Society, vol. 70(3), pages 971-1005, May.
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