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A minority game with bounded recall

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  • Renault, Jérôme
  • Scarsini, Marco
  • Tomala, Tristan

Abstract

This paper studies a repeated minority game with public signals, symmetric bounded recall, and pure strategies. We investigate both public and private equilibria of the game with fixed recall size. We first show how public equilibria in such a repeated game can be represented as colored subgraphs of a de Bruijn graph. Then we prove that the set of public equilibrium payoffs with bounded recall converges to the set of uniform equilibrium payoffs as the size of the recall increases. We also show that private equilibria behave badly: A private equilibrium payoff with bounded recall need not be a uniform equilibrium payoff.

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File URL: http://basepub.dauphine.fr/xmlui/bitstream/123456789/6381/2/2006-42.pdf
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Bibliographic Info

Paper provided by Université Paris-Dauphine in its series Open Access publications from Université Paris-Dauphine with number urn:hdl:123456789/6381.

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Date of creation: 2007
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Publication status: Published in Mathematics of Operations Research (2007) v.32, p.873-889
Handle: RePEc:ner:dauphi:urn:hdl:123456789/6381

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Related research

Keywords: folk theorem; de Bruijn sequence; imperfect monitoring; uniform equilibrium; public equilibrium; private equilibrium;

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References

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  1. Tristan Tomala, 1998. "Pure equilibria of repeated games with public observation," International Journal of Game Theory, Springer, vol. 27(1), pages 93-109.
  2. Ben-porath, Elchanan, 1990. "The complexity of computing a best response automaton in repeated games with mixed strategies," Games and Economic Behavior, Elsevier, vol. 2(1), pages 1-12, March.
  3. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
  4. Lehrer Ehud, 1994. "Finitely Many Players with Bounded Recall in Infinitely Repeated Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 390-405, November.
  5. Liaw, Sy-Sang & Liu, Ching, 2005. "The quasi-periodic time sequence of the population in minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 571-579.
  6. Levine, David & Fudenberg, Drew, 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Scholarly Articles 3203774, Harvard University Department of Economics.
  7. Cole, Harold L. & Kocherlakota, Narayana R., 2005. "Finite memory and imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 53(1), pages 59-72, October.
  8. Ehud Kalai & William Stanford, 1986. "Finite Rationality and Interpersonal Complexity in Repeated Games," Discussion Papers 679, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Michele Piccione & Ariel Rubinstein, 2003. "Modeling the Economic Interaction of Agents With Diverse Abilities to Recognize Equilibrium Patterns," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 212-223, 03.
  10. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 394, David K. Levine.
  11. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-81, November.
  12. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-11, May.
  13. 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.
  14. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
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Cited by:
  1. George J. Mailath & Wojciech Olszewski, 2008. "Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring," PIER Working Paper Archive 08-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  2. Scarsini, Marco & Renault, Jérôme & Tomala, Tristan, 2008. "Playing off-line games with bounded rationality," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/6127, Université Paris-Dauphine.

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