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Online Concealed Correlation by Boundedly Rational Players

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  • Gilad Bavly

    ()

  • Abraham Neyman

    ()

Abstract

In a repeated game with perfect monitoring, correlation among a group of players may evolve in the common course of play (online correlation). Such a correlation may be concealed from a boundedly rational player. The feasibility of such “online concealed correlation” is quantified by the individually rational payoff of the boundedly rational player. We show that “strong” players, i.e., players whose strategic complexity is less stringently bounded, can orchestrate online correlation of the actions of “weak” players, in a manner that is concealed from an opponent of “intermediate” strength. The result is illustrated in two models, each captures another aspect of bounded rationality. In the first, players use bounded recall strategies. In the second, players use strategies that are implementable by finite automata.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp336.

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Length: 36 pages
Date of creation: Sep 2003
Date of revision:
Handle: RePEc:huj:dispap:dp336

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References

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  1. GOSSNER, Olivier, 1998. "Repeated games played by cryptographically sophisticated players," CORE Discussion Papers 1998035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Olivier Gossner & Penelope Hernandez & Abraham Neyman, 2003. "Online Matching Pennies," Discussion Paper Series dp316, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  3. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  4. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  5. Gossner, Olivier & Tomala, Tristan, 2003. "Entropy and codification in repeated games with imperfect monitoring," Economics Papers from University Paris Dauphine 123456789/6885, Paris Dauphine University.
  6. Gilboa Itzhak & Schmeidler David, 1994. "Infinite Histories and Steady Orbits in Repeated Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 370-399, May.
  7. GOSSNER, Olivier & TOMALA, Tristan, 2003. "Entropy and codification in repeated games with imperfect monitoring," CORE Discussion Papers 2003033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Ehud Kalai, 1987. "Bounded Rationality and Strategic Complexity in Repeated Games," Discussion Papers 783, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
  10. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
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Cited by:
  1. Ron Peretz, 2013. "Correlation through bounded recall strategies," International Journal of Game Theory, Springer, vol. 42(4), pages 867-890, November.
  2. Ron Peretz, 2011. "Correlation through Bounded Recall Strategies," Discussion Paper Series dp579, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  3. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
  4. Peretz, Ron, 2012. "The strategic value of recall," Games and Economic Behavior, Elsevier, vol. 74(1), pages 332-351.
  5. Renault, Jérôme & Scarsini, Marco & Tomala, Tristan, 2008. "Playing off-line games with bounded rationality," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 207-223, September.
  6. Renault, Jérôme & Scarsini, Marco & Tomala, Tristan, 2007. "A minority game with bounded recall," Economics Papers from University Paris Dauphine 123456789/6381, Paris Dauphine University.
  7. George J. Mailath & : Wojciech Olszewski, 2008. "Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring, Second Version," PIER Working Paper Archive 08-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jul 2008.

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