IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

A folk theorem for minority games

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

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.

(This abstract was borrowed from another version of this item.)

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/B6WFW-4DWH09N-1/2/b506ff841c0ef171eff7d233cf52eebf
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 53 (2005)
Issue (Month): 2 (November)
Pages: 208-230

as
in new window

Handle: RePEc:eee:gamebe:v:53:y:2005:i:2:p:208-230
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

References listed on IDEAS
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.:

as in new window
  1. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005. "Certainty Independence and the Separation of Utility and Beliefs," Journal of Economic Theory, Elsevier, vol. 120(1), pages 129-136, January.
  2. 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.
  3. Lehrer, E, 1989. "Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-observable Actions," International Journal of Game Theory, Springer, vol. 18(1), pages 57-89.
  4. Maitreesh Ghatak & Massimo Morelli & Tomas Sjostrom, 2002. "Credit rationing, wealth inequality and allocation of talent," LSE Research Online Documents on Economics 5922, London School of Economics and Political Science, LSE Library.
  5. Abreu, Dilip & Milgrom, Paul & Pearce, David, 1991. "Information and Timing in Repeated Partnerships," Econometrica, Econometric Society, vol. 59(6), pages 1713-33, November.
  6. 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.
  7. W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
  8. Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers 1294, Cowles Foundation for Research in Economics, Yale University.
  9. Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2002. "Insurance Premia Consistent with the Market," ICER Working Papers - Applied Mathematics Series 24-2002, ICER - International Centre for Economic Research.
  10. Fabio Maccheroni, 2004. "Yaari's dual theory without the completeness axiom," Economic Theory, Springer, vol. 23(3), pages 701-714, March.
  11. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society.
  12. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-11, May.
  13. Umberto Cherubini & Elisa Luciano, 2002. "Multivariate Option Pricing with Copulas," ICER Working Papers - Applied Mathematics Series 05-2002, ICER - International Centre for Economic Research.
  14. Luigi Montrucchio & Fabio Privileggi, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," ICER Working Papers - Applied Mathematics Series 05-2001, ICER - International Centre for Economic Research.
  15. SORIN, Sylvain, 1988. "Repeated games with complete information," CORE Discussion Papers 1988022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. Renault, Jérôme, 2001. "3-player repeated games with lack of information on one side," Economics Papers from University Paris Dauphine 123456789/6538, Paris Dauphine University.
  17. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
  18. 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.
  19. Lehrer, Ehud, 1992. "On the Equilibrium Payoffs Set of Two Player Repeated Games with Imperfect Monitoring," International Journal of Game Theory, Springer, vol. 20(3), pages 211-26.
  20. Renault, Jerome & Tomala, Tristan, 2004. "Communication equilibrium payoffs in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 49(2), pages 313-344, November.
  21. Domenico Menicucci, 2003. "Optimal two-object auctions with synergies," Review of Economic Design, Springer, vol. 8(2), pages 143-164, October.
  22. Enrico Diecidue & Fabio Maccheroni, 2002. "Coherence without Additivity," ICER Working Papers - Applied Mathematics Series 10-2002, ICER - International Centre for Economic Research.
  23. Tristan Tomala, 1998. "Pure equilibria of repeated games with public observation," International Journal of Game Theory, Springer, vol. 27(1), pages 93-109.
  24. Umberto Cherubini & Elisa Luciano, 2002. "Pricing Vulnerable Options with Copulas," ICER Working Papers - Applied Mathematics Series 06-2002, ICER - International Centre for Economic Research.
  25. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2001. "A subjective spin on roulette wheels," ICER Working Papers - Applied Mathematics Series 17-2001, ICER - International Centre for Economic Research, revised Aug 2001.
  26. Massimo Marinacci & Fabio Maccheroni, 2002. "How to cut a pizza fairly: fair division with descreasing marginal evaluations," ICER Working Papers - Applied Mathematics Series 23-2002, ICER - International Centre for Economic Research.
  27. Guido Cozzi & Fabio Privileggi, 2002. "Wealth Polarization and Pulverization in Fractal Societies," ICER Working Papers - Applied Mathematics Series 39-2002, ICER - International Centre for Economic Research.
  28. 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.
  29. Lehrer, E, 1990. "Nash Equilibria of n-Player Repeated Games with Semi-standard Information," International Journal of Game Theory, Springer, vol. 19(2), pages 191-217.
  30. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
  31. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002. "Ambiguity from the Differential Viewpoint," ICER Working Papers - Applied Mathematics Series 17-2002, ICER - International Centre for Economic Research.
  32. 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.
  33. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.
  34. Haberman, Steven & Vigna, Elena, 2002. "Optimal investment strategies and risk measures in defined contribution pension schemes," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 35-69, August.
  35. 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.
  36. Renault, Jérôme, 2000. "On Two-Player Repeated Games with Lack of Information on One Side and State-Independent Signalling," Economics Papers from University Paris Dauphine 123456789/6109, Paris Dauphine University.
  37. Tomala, Tristan, 1999. "Nash Equilibria of Repeated Games with Observable Payoff Vectors," Games and Economic Behavior, Elsevier, vol. 28(2), pages 310-324, August.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:53:y:2005:i:2:p:208-230. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.