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An experimental study of information and mixed-strategy play in the three-person matching-pennies game

Author

Listed:
  • Arijit Mukherji

    (University of Minnesota, Minneapolis, MN 55455, USA)

  • Kevin A. McCabe

    (Economic Science Laboratory and Department of Economics, College of Business and Public Administration, University of Arizona, Tucson, AZ 85721, USA)

  • David E. Runkle

    (University of Minnesota, Minneapolis, MN 55455, USA)

Abstract

Recent experiments on mixed-strategy play in experimental games reject the hypothesis that subjects play a mixed strategy even when that strategy is the unique Nash equilibrium prediction. However, in a three-person matching-pennies game played with perfect monitoring and complete payoff information, we cannot reject the hypothesis that subjects play the mixed-strategy Nash equilibrium. Given this support for mixed-strategy play, we then consider two qualitatively different learning theories (sophisticated Bayesian and naive Bayesian) which predict that the amount of information given to subjects will determine whether they can learn to play the predicted mixed strategies. We reject the hypothesis that subjects play the symmetric mixed-strategy Nash equilibrium when they do not have complete payoff information. This finding suggests that players did not use sophisticated Bayesian learning to reach the mixed-strategy Nash equilibrium.

Suggested Citation

  • 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;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 421-462.
    • Handle: RePEc:spr:joecth:v:15:y:2000:i:2:p:421-462
    Note: Received: August 9, 1996; revised version: October 21, 1998
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    Citations

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    Cited by:

    1. Ofer Azar & Michael Bar-Eli, 2011. "Do soccer players play the mixed-strategy Nash equilibrium?," Applied Economics, Taylor & Francis Journals, vol. 43(25), pages 3591-3601.
    2. Johne Bone & Michalis Drouvelis & Indrajit Ray, 2013. "Coordination in 2 x 2 Games by Following Recommendations from Correlated Equilibria," Discussion Papers 12-04r, Department of Economics, University of Birmingham.
    3. Konstantinos Georgalos & Indrajit Ray & Sonali SenGupta, 2020. "Nash versus coarse correlation," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1178-1204, December.
    4. Antonio Cabrales & Michalis Drouvelis & Zeynep Gurguy & Indrajit Ray, 2017. "Transparency is Overrated: Communicating in a Coordination Game with Private Information," CESifo Working Paper Series 6781, CESifo.
    5. Georgalos, Konstantinos & Ray, Indrajit & Gupta, Sonali Sen, 2019. "Nash vs. Coarse Correlation," Cardiff Economics Working Papers E2019/3, Cardiff University, Cardiff Business School, Economics Section.
    6. Alessandro Rossi & Massimo Warglien, 2001. "An experimental Investigation of Fairness and Reciprocal Behavior in a Triangular Principal-Multiagent Relationship," ROCK Working Papers 014, Department of Computer and Management Sciences, University of Trento, Italy, revised 12 Jun 2008.
    7. Susumu Shikano & Michael F Stoffel & Markus Tepe, 2017. "Information accuracy in legislative oversight: Theoretical implications and experimental evidence," Rationality and Society, , vol. 29(2), pages 226-254, May.
    8. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Working Papers 19-2006, Singapore Management University, School of Economics.
    9. Ganna Pogrebna & Pavlo Blavatskyy, 2009. "Coordination, focal points and voting in strategic situations: a natural experiment," IEW - Working Papers 403, Institute for Empirical Research in Economics - University of Zurich.
    10. Tim Friehe, 2008. "Correlated payoffs in the inspection game: some theory and an application to corruption," Public Choice, Springer, vol. 137(1), pages 127-143, October.
    11. Aurora García-Gallego & Penelope Hernández-Rojas & Amalia Rodrigo-González, 2015. "An experimental online matching pennies game," Working Papers 2015/03, Economics Department, Universitat Jaume I, Castellón (Spain).
    12. Sijun Wang & Yuanjie He, 2008. "Compensating Nondedicated Cross-Functional Teams," Organization Science, INFORMS, vol. 19(5), pages 753-765, October.
    13. Weinstein-Gould Jesse, 2009. "Keeping the Hitter Off Balance: Mixed Strategies in Baseball," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(2), pages 1-20, May.
    14. Ganna Pogrebna & Pavlo Blavatskyy, 2009. "Coordination, focal points and voting in strategic situations: a natural experiment," Public Choice, Springer, vol. 140(1), pages 125-143, July.
    15. Johne Bone & Michalis Drouvelis & Indrajit Ray, 2013. "Coordination in 2 x 2 Games by Following Recommendations from Correlated Equilibria," Discussion Papers 12-04, Department of Economics, University of Birmingham.
    16. Jason Shachat & J. Todd Swarthout & Lijia Wei, 2011. "Man versus Nash An experiment on the self-enforcing nature of mixed strategy equilibrium," Working Papers 1101, Xiamen Unversity, The Wang Yanan Institute for Studies in Economics, Finance and Economics Experimental Laboratory, revised 21 Feb 2011.
    17. 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.
    18. Arijit Mukherji & David E. Runkle, 2000. "Learning to be unpredictable : an experimental study," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Spr), pages 14-20.
    19. Cabrales, Antonio & Drouvelis, Michalis & Gurguc, Zeynep & Ray, Indrajit, 2018. "Do we need to listen to all stakeholders?: communicating in a coordination game with private information," Cardiff Economics Working Papers E2018/23, Cardiff University, Cardiff Business School, Economics Section.

    More about this item

    Keywords

    Nash equilibrium; Bayesian learning; Experimental.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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