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

Author

Listed:
  • 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.

Suggested Citation

  • Thorsten Chmura & Werner Güth, 2011. "The Minority of Three-Game: An Experimental and Theoretical Analysis," Games, MDPI, vol. 2(3), pages 1-22, September.
    • Handle: RePEc:gam:jgames:v:2:y:2011:i:3:p:333-354:d:13920
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    References listed on IDEAS

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    1. Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
    2. 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, December.
    3. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    4. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    5. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    6. 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.
    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. 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, April.
    9. 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.
    10. 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 848-881, September.
    11. Sebastian Goerg & Reinhard Selten, 2009. "Experimental investigation of stationary concepts in cyclic duopoly games," Experimental Economics, Springer;Economic Science Association, vol. 12(3), pages 253-271, September.
    12. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
    13. 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.
    14. 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.
    15. 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 1041-1044, April.
    16. Reinhard Selten & Thorsten Chmura, 2008. "Stationary Concepts for Experimental 2x2-Games," American Economic Review, American Economic Association, vol. 98(3), pages 938-966, June.
    17. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    18. Giulio Bottazzi & Giovanna Devetag, 2007. "Competition and coordination in experimental minority games," Journal of Evolutionary Economics, Springer, vol. 17(3), pages 241-275, June.
    19. Greiner, Ben, 2004. "An Online Recruitment System for Economic Experiments," MPRA Paper 13513, University Library of Munich, Germany.
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    Cited by:

    1. Giovanna Devetag & Francesca Pancotto & Thomas Brenner, 2011. "The Minority Game Unpacked: Coordination and Competition in a Team-based Experiment," CEEL Working Papers 1102, Cognitive and Experimental Economics Laboratory, Department of Economics, University of Trento, Italia.
    2. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2023. "Strategy sets closed under payoff sampling," Games and Economic Behavior, Elsevier, vol. 138(C), pages 126-142.
    3. Yamada, Takashi & Hanaki, Nobuyuki, 2016. "An experiment on Lowest Unique Integer Games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 88-102.
    4. Linde, Jona & Sonnemans, Joep & Tuinstra, Jan, 2014. "Strategies and evolution in the minority game: A multi-round strategy experiment," Games and Economic Behavior, Elsevier, vol. 86(C), pages 77-95.
    5. Rapoport, Amnon & Gisches, Eyran J. & Daniel, Terry & Lindsey, Robin, 2014. "Pre-trip information and route-choice decisions with stochastic travel conditions: Experiment," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 154-172.
    6. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2020. "Stability for best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 185(C).
    7. Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2020. "Instability of Defection in the Prisoner’s Dilemma: Best Experienced Payoff Dynamics Analysis," MPRA Paper 99594, University Library of Munich, Germany.
    8. Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2021. "Instability of defection in the prisoner's dilemma under best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 197(C).
    9. Giovanna Devetag & Francesca Pancotto & Thomas Brenner, 2014. "The minority game unpacked:," Journal of Evolutionary Economics, Springer, vol. 24(4), pages 761-797, September.
    10. Sethi, Rajiv, 2021. "Stable sampling in repeated games," Journal of Economic Theory, Elsevier, vol. 197(C).
    11. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2022. "Stability of strict equilibria in best experienced payoff dynamics: Simple formulas and applications," Journal of Economic Theory, Elsevier, vol. 206(C).
    12. Christopher K. Hsee & Ying Zeng & Xilin Li & Alex Imas, 2021. "Bounded Rationality in Strategic Decisions: Undershooting in a Resource Pool-Choice Dilemma," Management Science, INFORMS, vol. 67(10), pages 6553-6567, October.
    13. Nadir Altinok & Abdurrahman Aydemir, 2015. "The Unfolding of Gender Gap in Education," Working Papers 934, Economic Research Forum, revised Aug 2015.
    14. Srinivas Arigapudi & Yuval Heller & Igal Milchtaich, 2020. "Instability of Defection in the Prisoner's Dilemma Under Best Experienced Payoff Dynamics," Papers 2005.05779, arXiv.org, revised Jan 2021.

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    More about this item

    Keywords

    coordination; minority game; mixed strategy; learning models; experiments;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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