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

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

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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 45 (2003)
Issue (Month): 1 (October)
Pages: 19-37

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Handle: RePEc:eee:gamebe:v:45:y:2003:i:1:p:19-37
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
  2. Keser, C. & Gardner, R., 1994. "Strategic Behavior of Experienced Subjects in a Common Pool Resource Game," Papers 94-009, Indiana - Center for Econometric Model Research.
  3. Dale O. Stahl & Paul W. Wilson, 2010. "On Players' Models of Other Players: Theory and Experimental Evidence," Levine's Working Paper Archive 542, David K. Levine.
  4. Stahl II, D.O., 1991. "Evolution of Smart Players," Papers 9166, Tilburg - Center for Economic Research.
  5. 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, June.
  6. Nagel, Rosemarie, 1993. "Experimental Results on Interactive Competitive Guessing," Discussion Paper Serie B 236, University of Bonn, Germany.
  7. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
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