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

  • Jason Shachat
  • J. Todd Swarthout
  • Lijia Wei

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://excen.gsu.edu/workingpapers/GSU_EXCEN_WP_2012-11.pdf
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Paper provided by Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University in its series Experimental Economics Center Working Paper Series with number 2012-11.

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Length: 26
Date of creation: Jul 2012
Date of revision:
Handle: RePEc:exc:wpaper:2012-11
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  1. repec:spr:compst:v:59:y:2004:i:3:p:359-373 is not listed on IDEAS
  2. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, vol. 104(1), pages 189-226, May.
  3. Ochs Jack, 1995. "Games with Unique, Mixed Strategy Equilibria: An Experimental Study," Games and Economic Behavior, Elsevier, vol. 10(1), pages 202-217, July.
  4. Jason Shachat & J. Todd Swarthout, 2004. "Do we detect and exploit mixed strategy play by opponents?," Mathematical Methods of Operations Research, Springer, vol. 59(3), pages 359-373, 07.
  5. 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.
  6. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
  7. Charles Noussair & Marc Willinger, 2011. "Mixed strategies in an unprofitable game: an experiment," Working Papers 11-19, LAMETA, Universtiy of Montpellier, revised Nov 2011.
  8. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
  9. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," Review of Economic Studies, Wiley Blackwell, vol. 70(2), pages 395-415, 04.
  10. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
  11. Binmore, Ken & Swierzbinski, Joe & Proulx, Chris, 2001. "Does Minimax Work? An Experimental Study," Economic Journal, Royal Economic Society, vol. 111(473), pages 445-64, July.
  12. Reinhard Selten & Thorsten Chmura, 2005. "Stationary Concepts for Experimental 2x2 Games," Bonn Econ Discussion Papers bgse33_2005, University of Bonn, Germany.
  13. Robert W. Rosenthal & Jason Shachat & Mark Walker, 2003. "Hide and seek in Arizona," International Journal of Game Theory, Springer, vol. 32(2), pages 273-293, December.
  14. Morgan, John & Sefton, Martin, 2002. "An Experimental Investigation of Unprofitable Games," Games and Economic Behavior, Elsevier, vol. 40(1), pages 123-146, July.
  15. 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.
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