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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 39896.

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Date of creation: 07 Jul 2012
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Handle: RePEc:pra:mprapa:39896

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Keywords: Mixed Strategy; Experiment; Hidden Markov Model;

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  1. Robert W. Rosenthal & Jason Shachat & Mark Walker, 2003. "Hide and Seek in Arizona," Experimental 0312001, EconWPA.
  2. 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.
  3. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," Review of Economic Studies, Wiley Blackwell, vol. 70(2), pages 395-415, 04.
  4. Reinhard Selten & Thorsten Chmura, 2005. "Stationary Concepts for Experimental 2x2 Games," Bonn Econ Discussion Papers bgse33_2005, University of Bonn, Germany.
  5. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
  6. 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.
  7. Ochs Jack, 1995. "Games with Unique, Mixed Strategy Equilibria: An Experimental Study," Games and Economic Behavior, Elsevier, vol. 10(1), pages 202-217, July.
  8. Morgan, John & Sefton, Martin, 2002. "An Experimental Investigation of Unprofitable Games," Games and Economic Behavior, Elsevier, vol. 40(1), pages 123-146, July.
  9. Charles Noussair & Marc Willinger, 2011. "Mixed strategies in an unprofitable game: an experiment," Working Papers 11-19, LAMETA, Universtiy of Montpellier, revised Nov 2011.
  10. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
  11. Jason Shachat & J. Todd Swarthout, 2003. "Do We Detect and Exploit Mixed Strategy Play by Opponents?," Experimental 0310001, EconWPA.
  12. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
  13. 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.
  14. 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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