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Online Concealed Correlation by Boundedly Rational Players

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  • Gilad Bavly

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  • Abraham Neyman

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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.

Suggested Citation

  • Gilad Bavly & Abraham Neyman, 2003. "Online Concealed Correlation by Boundedly Rational Players," Discussion Paper Series dp336, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp336
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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/Neyman336.pdf
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/6885 is not listed on IDEAS
    2. Olivier Gossner & Penelope Hernandez & Abraham Neyman, 2003. "Online Matching Pennies," Discussion Paper Series dp316, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    3. 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.
    4. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    5. 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).
    6. 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.
    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. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
    9. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
    10. 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. repec:dau:papers:123456789/6127 is not listed on IDEAS
    2. Peretz, Ron, 2012. "The strategic value of recall," Games and Economic Behavior, Elsevier, vol. 74(1), pages 332-351.
    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. 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.
    5. Ron Peretz, 2013. "Correlation through bounded recall strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 867-890, November.
    6. Bavly, Gilad & Neyman, Abraham, 2014. "Online concealed correlation and bounded rationality," Games and Economic Behavior, Elsevier, vol. 88(C), pages 71-89.
    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.
    8. repec:dau:papers:123456789/6381 is not listed on IDEAS
    9. Ron Peretz, 2011. "Correlation through Bounded Recall Strategies," Discussion Paper Series dp579, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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