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A folk theorem for minority games

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Author Info
Jerome Renault ()
Sergio Scarlatti ()
Marco Scarsini ()

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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”). Between the stages, only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payo can be achieved as a uniform equilibrium payo , and as an almost sure equilibrium payo . 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 a unusual way, the pure actions that were played before start of the punishment.

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Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 10-2003.

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Length: 26 pages
Date of creation: Jan 2003
Date of revision:
Handle: RePEc:icr:wpmath:10-2003

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Keywords: Repeated games; imperfect monitoring; public signals;

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  2. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo & Siniscalchi, Marciano, 2001. "A Subjective Spin on Roulette Wheels," Working Papers 1127, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  3. Massimo Marinacci & Luigi Montrucchio, 2003. "Cores and stable sets of finite dimensional games," ICER Working Papers - Applied Mathematics Series 07-2003, ICER - International Centre for Economic Research. [Downloadable!]
  4. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October. [Downloadable!] (restricted)
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  7. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November. [Downloadable!] (restricted)
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  8. Adriana Castaldo & Massimo Marinacci, 2001. "Random correspndences as bundles of random variables," ICER Working Papers - Applied Mathematics Series 12-2001, ICER - International Centre for Economic Research. [Downloadable!]
  9. Umberto Cherubini & Elisa Luciano, 2002. "Pricing Vulnerable Options with Copulas," ICER Working Papers - Applied Mathematics Series 06-2002, ICER - International Centre for Economic Research. [Downloadable!]
  10. Fabio Maccheroni & Fabio Maccheroni & Massimo Marinacci & Massimo Marinacci, 2003. "How to cut a pizza fairly: Fair division with decreasing marginal evaluations," Social Choice and Welfare, Springer, vol. 20(3), pages 457-465, 06. [Downloadable!] (restricted)
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  12. Marinacci, Massimo & Montrucchio, Luigi, 2004. "A characterization of the core of convex games through Gateaux derivatives," Journal of Economic Theory, Elsevier, vol. 116(2), pages 229-248, June. [Downloadable!] (restricted)
  13. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Ambiguity from the Differential Viewpoint," Working Papers 1130, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  14. Juan Dubra & Fabio Maccheroni & Efe Oki, 2001. "Expected utility theory without the completeness axiom," ICER Working Papers - Applied Mathematics Series 11-2001, ICER - International Centre for Economic Research. [Downloadable!]
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  15. Umberto Cherubini & Elisa Luciano, 2002. "Multivariate Option Pricing with Copulas," ICER Working Papers - Applied Mathematics Series 05-2002, ICER - International Centre for Economic Research. [Downloadable!]
  16. Fabio Maccheroni & William H. Ruckle, 2001. "BV as a dual space," ICER Working Papers - Applied Mathematics Series 29-2001, ICER - International Centre for Economic Research. [Downloadable!]
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  18. 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. [Downloadable!] (restricted)
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  19. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Bibliography 7616, UCLA Department of Economics. [Downloadable!]
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  20. Claudio Mattalia, 2003. "Existence of solutions and asset pricing bubbles in general equilibrium models," ICER Working Papers - Applied Mathematics Series 02-2003, ICER - International Centre for Economic Research. [Downloadable!]
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  22. Maitreesh Ghatak & Massimo Morelli & Tomas Sjoström, 2001. "Credit rationing, wealth inequality, and allocation of talent," ICER Working Papers - Applied Mathematics Series 23-2001, ICER - International Centre for Economic Research. [Downloadable!]
  23. Fabio Maccheroni, 2000. "Yaari dual theory without the completeness axiom," ICER Working Papers - Applied Mathematics Series 30-2001, ICER - International Centre for Economic Research, revised Oct 2001. [Downloadable!]
Full references

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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
  2. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
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  3. Thibault Gajdos & Eric Maurin, 2002. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," ICER Working Papers - Applied Mathematics Series 15-2003, ICER - International Centre for Economic Research, revised Mar 2003. [Downloadable!]
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  4. Kets, W., 2007. "The Minority Game: An Economics Perspective," Discussion Paper 2007-53, Tilburg University, Center for Economic Research. [Downloadable!]
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  5. 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. [Downloadable!]
  6. Alfred Müller & Marco Scarsini, 2003. "Archimedean Copulae and Positive Dependence," ICER Working Papers - Applied Mathematics Series 25-2003, ICER - International Centre for Economic Research. [Downloadable!]
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  7. Ted Theodosopoulos & Ming Yuen, 2006. "Imbalance attractors for a strategic model of market microstructure," Quantitative Finance Papers math/0605421, arXiv.org. [Downloadable!]
  8. 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. [Downloadable!]
  9. Kets, W. & Voorneveld, M., 2007. "Congestion, Equilibrium and Learning: The Minority Game," Discussion Paper 2007-61, Tilburg University, Center for Economic Research. [Downloadable!]
  10. 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. [Downloadable!]
  11. Jerome Renault & Sergio Scarlatti & Marco Scarsini, 2003. "A folk theorem for minority games," ICER Working Papers - Applied Mathematics Series 10-2003, ICER - International Centre for Economic Research. [Downloadable!]
    Other versions:
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