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How to play (3 x 3)-games.: A strategy method experiment

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  • Selten, Reinhard
  • Abbink, Klaus
  • Buchta, Joachim
  • Sadrieh, Abdolkarim

Abstract

Using the strategy method (Selten 1967) we elicit subjects' strategies for playing any 2-person 3x3-game with integer payoffs between 0 and 99.In each of 5 tournaments, every strategy pair plays 500000 games.The frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, with the equilibria that maximize joint payoff being preferred when multiple exist.For games without pure equilibria, strategies are typically based on elements of the best-reply cascade: MAP (maximize the expected payoff against uniformly randomizing opponents), BR-MAP (best reply to MAP), and BR-BR-MAP (best reply to BR-MAP).
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Suggested Citation

  • Selten, Reinhard & Abbink, Klaus & Buchta, Joachim & Sadrieh, Abdolkarim, 2003. "How to play (3 x 3)-games.: A strategy method experiment," Games and Economic Behavior, Elsevier, vol. 45(1), pages 19-37, October.
  • Handle: RePEc:eee:gamebe:v:45:y:2003:i:1:p:19-37
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    References listed on IDEAS

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    1. Claudia Keser & Roy Gardner, 1999. "Strategic behavior of experienced subjects in a common pool resource game," International Journal of Game Theory, Springer;Game Theory Society, pages 241-252.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, January.
    3. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
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    6. Claudia Keser & Roy Gardner, 1999. "Strategic behavior of experienced subjects in a common pool resource game," International Journal of Game Theory, Springer;Game Theory Society, pages 241-252.
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    8. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, pages 218-254.
    9. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, pages 1313-1326.
    10. Nagel, Rosemarie, 1993. "Experimental Results on Interactive Competitive Guessing," Discussion Paper Serie B 236, University of Bonn, Germany.
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    Cited by:

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    2. Roy Gardner, 2007. "Michael Bacharach, Beyond Individual Choice: Teams and Frames in Game Theory. Princeton, NJ: Princeton University Press, 2006. xxiii + 214 pages. USD 35.00 (cloth)," Public Choice, Springer, vol. 130(3), pages 495-497, March.
    3. Boone, Jan & Sadrieh, Abdolkarim & van Ours, Jan C., 2009. "Experiments on unemployment benefit sanctions and job search behavior," European Economic Review, Elsevier, pages 937-951.
    4. Grimm, Veronika & Mengel, Friederike, 2012. "An experiment on learning in a multiple games environment," Journal of Economic Theory, Elsevier, pages 2220-2259.
    5. Jordi Brandts & Gary Charness, 2011. "The strategy versus the direct-response method: a first survey of experimental comparisons," Experimental Economics, Springer;Economic Science Association, pages 375-398.
    6. Huck, Steffen & Oechssler, Jorg, 2000. "Informational cascades in the laboratory: Do they occur for the right reasons?," Journal of Economic Psychology, Elsevier, pages 661-671.
    7. Stahl, Dale O. & Haruvy, Ernan, 2008. "Level-n bounded rationality and dominated strategies in normal-form games," Journal of Economic Behavior & Organization, Elsevier, pages 226-232.
    8. Annamaria Nese & Arturo Palomba & Patrizia Sbriglia & Maurizio Scudiero, 2013. "Third party punishment and criminal behavior: an experiment with the Italian Camorra prison inmates," Economics Bulletin, AccessEcon, vol. 33(3), pages 1875-1884.
    9. Olivier Armantier, 2006. "Do Wealth Differences Affect Fairness Considerations?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 391-429, May.
    10. Grimm, Veronika & Mengel, Friederike, 2012. "An experiment on learning in a multiple games environment," Journal of Economic Theory, Elsevier, pages 2220-2259.
    11. Staffiero, Gianandrea, 2006. "Helping the meaner, hurting the nicer: The contribution versus distribution game," IESE Research Papers D/652, IESE Business School.
    12. Dufwenberg, Martin & Sundaram, Ramya & Butler, David J., 2010. "Epiphany in the Game of 21," Journal of Economic Behavior & Organization, Elsevier, pages 132-143.
    13. Spiwoks, Markus & Bizer, Kilian & Hein, Oliver, 2008. "Informational cascades: A mirage?," Journal of Economic Behavior & Organization, Elsevier, pages 193-199.
    14. Armantier, Olivier, 2004. "Does observation influence learning?," Games and Economic Behavior, Elsevier, vol. 46(2), pages 221-239, February.
    15. John D. Hey & Daniela Di Cagno, 2016. "Does money impede convergence?," Experimental Economics, Springer;Economic Science Association, pages 595-612.
    16. Bogliacino, Francesco & Grimalda, Gianluca & Jimenez, Laura, 2017. "Consultative Democracy & Trust," MPRA Paper 82138, University Library of Munich, Germany.
    17. Huck, Steffen & Muller, Wieland, 2000. "Perfect versus Imperfect Observability--An Experimental Test of Bagwell's Result," Games and Economic Behavior, Elsevier, vol. 31(2), pages 174-190, May.
    18. Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, pages 311-333.

    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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