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How to Play 3x3 Games : A Strategy Method Experiment

Author

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  • Selten, R.
  • Abbink, K.
  • Buchta, J.
  • Sadrieh, A.

    (Tilburg University, School of Economics and Management)

Abstract

We report an experiment that uses the strategy method (Selten 1967) to elicit subjects' general strategy for playing any 2-person 3x3-game with integer payoffs between 0 and 99. Each two subjects' strategies play 500000 games in each of the 5 tournaments. For games with pure strategy equilibria (ca. 80%), the frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, in which there is equilibrium play in 98% of all games with only one pure equilibrium. In games with more than one pure equilibrium, a tendency towards the selection of the one with the maximum joint payoff is observed. For games without pure equilibria, subjects’ strategies do not search for mixed equilibria. The strategy programs are based on much simpler strategic concepts combined in various ways. The simplest one is MAP, maximal average payoff, the strategy which maximizes the sum of the three payoffs obtainable against the possible choices of the other player. BR-MAP, the best reply to MAP, and BR-BR-MAP, the best reply to BR-MAP, are also important ingredients of the strategy programs. Together these three form a hierarchy to which we refer to as the best-reply cascade.
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Suggested Citation

  • Selten, R. & Abbink, K. & Buchta, J. & Sadrieh, A., 2002. "How to Play 3x3 Games : A Strategy Method Experiment," Other publications TiSEM 6ef71dcd-3f97-4d13-b75a-2, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:6ef71dcd-3f97-4d13-b75a-206a2609a2a4
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    References listed on IDEAS

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    8. Grimm, Veronika & Mengel, Friederike, 2012. "An experiment on learning in a multiple games environment," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2220-2259.
    9. Staffiero, Gianandrea, 2006. "Helping the meaner, hurting the nicer: The contribution versus distribution game," IESE Research Papers D/652, IESE Business School.
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    12. Daniela Di Cagno & Werner Güth & Giacomo Sillari, 2015. "The better toolbox: Experimental Methodology in Economics and Psychology," Working Papers CESARE 2/2015, Dipartimento di Economia e Finanza, LUISS Guido Carli.
    13. Bettina Rockenbach & Irenaeus Wolff, 2016. "Designing Institutions for Social Dilemmas," German Economic Review, Verein für Socialpolitik, vol. 17(3), pages 316-336, August.
    14. Hugh Kelley, 2014. "Experimental Study of Firm Bounded Rationality and the Pattern of Trade," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(4), pages 969-1006, December.
    15. Francesco Bogliacino & Laura Jiménez & Gianluca Grimalda, 2015. "Consultative, Democracy and Trust," Documentos de Trabajo, Escuela de Economía 12696, Universidad Nacional de Colombia, FCE, CID.
    16. Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May.
    17. Jordi Brandts & Gary Charness, 2011. "The strategy versus the direct-response method: a first survey of experimental comparisons," Experimental Economics, Springer;Economic Science Association, vol. 14(3), pages 375-398, September.
    18. Stahl, Dale O. & Haruvy, Ernan, 2008. "Level-n bounded rationality and dominated strategies in normal-form games," Journal of Economic Behavior & Organization, Elsevier, vol. 66(2), pages 226-232, May.
    19. 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.
    20. Dufwenberg, Martin & Sundaram, Ramya & Butler, David J., 2010. "Epiphany in the Game of 21," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 132-143, August.
    21. Ayala Arad & Ariel Rubinstein, 2012. "The 11-20 Money Request Game: A Level-k Reasoning Study," American Economic Review, American Economic Association, vol. 102(7), pages 3561-3573, December.
    22. Spiwoks, Markus & Bizer, Kilian & Hein, Oliver, 2008. "Informational cascades: A mirage?," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 193-199, July.
    23. Olivier Armantier, 2001. "Does Wealth Affect Fairness Considerations?," Department of Economics Working Papers 01-05, Stony Brook University, Department of Economics.
    24. Bogliacino, Francesco & Grimalda, Gianluca & Jimenez, Laura, 2017. "Consultative Democracy & Trust," MPRA Paper 82138, University Library of Munich, Germany.
    25. Karen Pittel & Dirk Rübbelke, 2012. "Transitions in the negotiations on climate change: from prisoner’s dilemma to chicken and beyond," International Environmental Agreements: Politics, Law and Economics, Springer, vol. 12(1), pages 23-39, March.

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    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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