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The Minority of Three-Game: An Experimental and Theoretical Analysis

  • Thorsten Chmura

    (Department of Economics, University of Munich)

  • Werner Güth

    ()

    (Max Planck Institute of Economics, Strategic Interaction Group)

  • Thomas Pitz

    (Nottingham University Business School China)

  • Anthony Ziegelmeyer

    (Max Planck Institute of Economics, Strategic Interaction Group)

We report experimental and theoretical results on the minority of three-game where three players have to choose one of two alternatives independently and the most rewarding alternative is the one chosen by a single player. This coordination game has many asymmetric equilibria in pure strategies that are non strict and payoff-asymmetric, and a unique symmetric mixed strategy equilibrium in which each player's behavior is based on the toss of a fair coin. We show that such a straightforward behavior is predicted by Harsanyi and Selten's (1988) equilibrium selection theory as well as alternative solution concepts like impulse balance equilibrium and sampling equilibrium. Our results indicate that participants rely on various decision rules, and that only a quarter of them decide according to the toss of a fair coin. Reinforcement learning is the most successful decision rule as it describes best the behavior of about a third of our participants.

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Paper provided by Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics in its series Jena Economic Research Papers with number 2010-071.

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Date of creation: 19 Oct 2010
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Handle: RePEc:jrp:jrpwrp:2010-071
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  1. Giulio Bottazzi & Giovanna Devetag, 2007. "Competition and coordination in experimental minority games," Journal of Evolutionary Economics, Springer, vol. 17(3), pages 241-275, June.
  2. John Duffy & Ed Hopkins, 2004. "Learning, Information and Sorting in Market Entry Games: Theory and Evidence," ESE Discussion Papers 78, Edinburgh School of Economics, University of Edinburgh.
  3. Reinhard Selten & Thorsten Chmura, 2005. "Stationary Concepts for Experimental 2x2 Games," Bonn Econ Discussion Papers bgse33_2005, University of Bonn, Germany.
  4. Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
  5. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-47, September.
  6. Dittrich, Dennis Alexis Valin & Güth, Werner & Kocher, Martin G. & Pezanis-Christou, Paul, 2012. "Loss aversion and learning to bid," Munich Reprints in Economics 18205, University of Munich, Department of Economics.
    • Dennis A. V. Dittrich & Werner Güth & Martin G. Kocher & Paul Pezanis‐Christou, 2012. "Loss Aversion and Learning to Bid," Economica, London School of Economics and Political Science, vol. 79(314), pages 226-257, 04.
  7. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
  8. Thorsten Chmura, 2011. "Response Modes And Coordination In A Traffic Context, An Experimental Comparison Of Chinese And German Participants," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 56(04), pages 489-501.
  9. Selten, R. & Chmura, T. & Pitz, T. & Kube, S. & Schreckenberg, M., 2007. "Commuters route choice behaviour," Games and Economic Behavior, Elsevier, vol. 58(2), pages 394-406, February.
  10. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April.
  11. Sebastian Goerg & Reinhard Selten, 2009. "Experimental investigation of stationary concepts in cyclic duopoly games," Experimental Economics, Springer, vol. 12(3), pages 253-271, September.
  12. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer, vol. 10(2), pages 171-178, June.
  13. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
  14. Reinhard Selten & Thorsten Chmura & Sebastian J. Goerg, 2011. "Stationary Concepts for Experimental 2 X 2 Games: Reply," American Economic Review, American Economic Association, vol. 101(2), pages 1041-44, April.
  15. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
  16. Chmura, T. & Pitz, T., 2006. "Successful strategies in repeated minority games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 477-480.
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