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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

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, 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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    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, vol. 28(2), 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, December.
    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.
    4. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    5. Stahl Dale O., 1993. "Evolution of Smartn Players," Games and Economic Behavior, Elsevier, vol. 5(4), pages 604-617, October.
    6. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    7. Nagel, Rosemarie, 1993. "Experimental Results on Interactive Competitive Guessing," Discussion Paper Serie B 236, University of Bonn, Germany.
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    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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