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

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  • Thorsten Chmura

    ()
    (Department of Economics, University of Munich, Ludwigstrasse 59, Munich 80539, Germany)

  • Werner Güth

    ()
    (Strategic Interaction Group, Max Planck Institute of Economics, Kahlaische Str. 10, Jena 07745, Germany)

Abstract

We report experimental results on the minority of three-game, where three players choose one of two alternatives 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. This straightforward behavior is predicted by equilibrium selection, impulse-balance equilibrium, and payoff-sampling equilibrium. Experimental participants rely on various decision rules, and only a quarter of them perfectly randomize.

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Bibliographic Info

Article provided by MDPI, Open Access Journal in its journal Games.

Volume (Year): 2 (2011)
Issue (Month): 3 (September)
Pages: 333-354

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Handle: RePEc:gam:jgames:v:2:y:2011:i:3:p:333-354:d:13920

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Keywords: coordination; minority game; mixed strategy; learning models; experiments;

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References

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  1. 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.
  2. John Duffy & Ed Hopkins, 2010. "Learning, Information and Sorting in Market Entry Games: Theory and Evidence," Levine's Working Paper Archive 506439000000000355, David K. Levine.
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  4. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-47, September.
  5. Rajiv Sethi, 1998. "Stability of Equilibria in Games with Procedurally Rational Players," Game Theory and Information 9811003, EconWPA, revised 04 Mar 1999.
  6. 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.
  7. Reinhard Selten & Thorsten Chmura, 2005. "Stationary Concepts for Experimental 2x2 Games," Bonn Econ Discussion Papers bgse33_2005, University of Bonn, Germany.
  8. 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.
  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. 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.
  11. 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.
  12. Sebastian Goerg & Reinhard Selten, 2009. "Experimental investigation of stationary concepts in cyclic duopoly games," Experimental Economics, Springer, vol. 12(3), pages 253-271, September.
  13. 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.
  14. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
  15. Giulio Bottazzi & Giovanna Devetag, 2007. "Competition and coordination in experimental minority games," Journal of Evolutionary Economics, Springer, vol. 17(3), pages 241-275, June.
  16. 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.
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Cited by:
  1. Sonnemans, J. & Tuinstra, J. & Linde, J., 2013. "Strategies and Evolution in the Minority Game: A Multi- Round Strategy Experiment," CeNDEF Working Papers 13-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  2. G. Devetag & F. Pancotto & T. Brenner, 2011. "The Minority Game Unpacked: Coordination and Competition in a Team-based Experiment," Working Papers wp770, Dipartimento Scienze Economiche, Universita' di Bologna.
  3. Jona Linde & Joep Sonnemans & Jan Tuinstra, 2013. "Strategies and Evolution in the Minority Game: A Multi- Round Strategy Experiment," Tinbergen Institute Discussion Papers 13-043/I, Tinbergen Institute.

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