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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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Related research

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

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References

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  1. Duffy, John & Hopkins, Ed, 2005. "Learning, information, and sorting in market entry games: theory and evidence," Games and Economic Behavior, Elsevier, vol. 51(1), pages 31-62, April.
  2. 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.
  3. Giulio Bottazzi & Giovanna Devetag, 2007. "Competition and coordination in experimental minority games," Journal of Evolutionary Economics, Springer, vol. 17(3), pages 241-275, June.
  4. Dennis A. V. Dittrich & Werner Güth & Martin Kocher & Paul Pezanis-Christou, . "Loss aversion and learning to bid," Papers on Strategic Interaction 2005-03, Max Planck Institute of Economics, Strategic Interaction Group.
    • 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.
  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. Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
  7. Sebastian Goerg & Reinhard Selten, 2009. "Experimental investigation of stationary concepts in cyclic duopoly games," Experimental Economics, Springer, vol. 12(3), pages 253-271, September.
  8. 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.
  9. 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.
  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. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer, vol. 10(2), pages 171-178, June.
  13. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
  14. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-66, June.
  15. 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.
  16. 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.
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Cited by:
  1. 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.
  2. Giovanna Devetag & Francesca Pancotto & Thomas Brenner, 2011. "The Minority Game Unpacked: Coordination and Competition in a Team-based Experiment," LEM Papers Series 2011/18, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  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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