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A folk theorem for minority games

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  • Renault, Jerome
  • Scarlatti, Sergio
  • Scarsini, Marco

Abstract

We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payoff can be achieved as a uniform equilibrium payoff, and as an almost sure equilibrium payoff. In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in an unusual way, the pure actions that were played before the start of the punishment.
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  • Renault, Jerome & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 208-230, November.
  • Handle: RePEc:eee:gamebe:v:53:y:2005:i:2:p:208-230
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    Cited by:

    1. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003.
    2. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    3. Kets, W., 2007. "The Minority Game : An Economics Perspective," Discussion Paper 2007-53, Tilburg University, Center for Economic Research.
    4. Renault, Jerome & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 208-230, November.
    5. repec:dau:papers:123456789/2347 is not listed on IDEAS
    6. Gajdos, Thibault & Tallon, Jean-Marc & Vergnaud, Jean-Christophe, 2004. "Decision making with imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 647-681, September.
    7. Kets, W., 2008. "Networks and learning in game theory," Other publications TiSEM 7713fce1-3131-498c-8c6f-3, Tilburg University, School of Economics and Management.
    8. Kets, W. & Voorneveld, M., 2007. "Congestion, Equilibrium and Learning : The Minority Game," Discussion Paper 2007-61, Tilburg University, Center for Economic Research.
    9. Jérôme Renault & Tristan Tomala, 2011. "General Properties of Long-Run Supergames," Dynamic Games and Applications, Springer, vol. 1(2), pages 319-350, June.
    10. Iván Arribas & Amparo Urbano Salvador, 2014. "Local coordination and global congestion in random networks," Discussion Papers in Economic Behaviour 0814, University of Valencia, ERI-CES.
    11. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    12. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research.
    13. Renault, Jérôme & Scarlatti, Sergio & Scarsini, Marco, 2008. "Discounted and finitely repeated minority games with public signals," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 44-74, July.
    14. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research.
    15. 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.
    16. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research.
    17. repec:dau:papers:123456789/6381 is not listed on IDEAS
    18. Ted Theodosopoulos & Ming Yuen, 2006. "Imbalance attractors for a strategic model of market microstructure," Papers math/0605421, arXiv.org.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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