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How to Play 3x3-Games A Strategy Method Experiment

Author

Listed:
  • 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.

Suggested Citation

  • Selten, Reinhard & Abbink, Klaus & Buchta, Joachim & Sadrieh, Abdolkarim, 2000. "How to Play 3x3-Games A Strategy Method Experiment," Bonn Econ Discussion Papers 3/2001, University of Bonn, Bonn Graduate School of Economics (BGSE).
    • Handle: RePEc:zbw:bonedp:32001
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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, vol. 28(2), pages 241-252.
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    Keywords

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    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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