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Man versus Nash An experiment on the self-enforcing nature of mixed strategy equilibrium

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Author Info

  • Jason Shachat

    ()
    (Wang Yanan Institute for Studies in Economics and MOE Key Laboratory in Econometrics, Xiamen University)

  • J. Todd Swarthout

    ()
    (Department of Economics, Georgia State University)

  • Lijia Wei

    ()
    (Wang Yanan Institute for Studies in Economics, Xiamen University)

Abstract

We examine experimentally how humans behave when they play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects’ play was consistent with their Nash equilibrium strategy, while a larger percentage of subjects’ play was more consistent with different models of play: equiprobable play for the zero-sum game, and the minimax strategy in the unprofitable game. We estimate the heterogeneity and dynamics of the subjects’ latent mixed strategy sequences via a hidden Markov model. This provides clear results on the identification of the use of pure and mixed strategies and the limiting distribution over strategies. The mixed strategy Nash equilibrium is not self-enforcing except when it coincides with the equal probability mixed strategy, and there is surprising amounts of pure strategy play and clear cycling between the pure strategy states.

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File URL: http://feel.xmu.edu.cn/RePEc/wpaper/Man_Versus_Nash.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 1101.

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Length: 29 pages
Date of creation: 21 Feb 2011
Date of revision: 21 Feb 2011
Handle: RePEc:fee:wpaper:1101

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Related research

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

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References

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  1. Jason Shachat & J. Todd Swarthout, 2002. "Learning about Learning in Games through Experimental Control of Strategic Interdependence," Experimental Economics Center Working Paper Series, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University 2006-17, Experimental Economics Center, Andrew Young School of Policy Studies, Georgia State University, revised Aug 2008.
  2. Peter Duersch & Albert Kolb & Joerg Oechssler & Burkhard Schipper, 2005. "Rage Against the Machines: How Subjects Learn to Play Against Computers," Game Theory and Information, EconWPA 0510012, EconWPA.
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  4. Jason Shachat & J. Todd Swarthout, 2003. "Do We Detect and Exploit Mixed Strategy Play by Opponents?," Experimental, EconWPA 0310001, EconWPA.
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  7. Robert W. Rosenthal & Jason Shachat & Mark Walker, 2003. "Hide and Seek in Arizona," Experimental, EconWPA 0312001, EconWPA.
  8. Duffy, John, 2006. "Agent-Based Models and Human Subject Experiments," Handbook of Computational Economics, Elsevier, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 19, pages 949-1011 Elsevier.
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  11. Reinhard Selten & Thorsten Chmura, 2005. "Stationary Concepts for Experimental 2x2 Games," Bonn Econ Discussion Papers, University of Bonn, Germany bgse33_2005, University of Bonn, Germany.
  12. R. J. Aumann & M. Maschler, 1972. "Some Thoughts on the Minimax Principle," Management Science, INFORMS, INFORMS, vol. 18(5-Part-2), pages 54-63, January.
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  16. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, Econometric Society, vol. 58(5), pages 1065-81, September.
  17. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, Elsevier, vol. 104(1), pages 189-226, May.
  18. Spiliopoulos, Leonidas, 2008. "Humans versus computer algorithms in repeated mixed strategy games," MPRA Paper 6672, University Library of Munich, Germany.
  19. Arijit Mukherji & Kevin A. McCabe & David E. Runkle, 2000. "An experimental study of information and mixed-strategy play in the three-person matching-pennies game," Economic Theory, Springer, Springer, vol. 15(2), pages 421-462.
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Cited by:
  1. Jason Shachat & J. Todd Swarthout, 2003. "Learning about Learning in Games through Experimental Control of Strategic Interdependence," Experimental, EconWPA 0310003, EconWPA.

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