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Online Concealed Correlation and Bounded Rationality

  • Gilad Bavly
  • Abraham Neyman

Correlation of players' actions may evolve in the common course of the play of a repeated game with perfect monitoring (``obline correlation''). In this paper we study the concealment of such correlation from a boundedly rational player. We show that ``strong'' players, i.e., players whose strategic complexity is less stringently bounded, can orchestrate the obline correlation of the actions of ``weak'' players, where this correlation is concealed from an opponent of ``intermediate'' strength. The feasibility of such ``\ol concealed correlation'' is reflected in the individually rational payoff of the opponent and in the equilibrium payoffs of the repeated game. This result enables the derivation of a folk theorem that characterizes the set of equilibrium payoffs in a class of repeated games with boundedly rational players and a mechanism designer who sends public signals. The result is illustrated in two models, each of which captures a different 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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Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp659.

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Length: 46 pages
Date of creation: Feb 2014
Date of revision:
Handle: RePEc:huj:dispap:dp659
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  1. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  2. O. Gossner, 1999. "Repeated games played by cryptographically sophisticated players," THEMA Working Papers 99-07, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  3. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  4. Itzhak Gilboa & David Schmeidler, 1989. "Infinite Histories and Steady Orbits in Repeated Games," Discussion Papers 846, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Olivier Gossner & Penelope Hernandez & Abraham Neyman, 2004. "Optimal Use of Communication Resources," Discussion Paper Series dp377, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  6. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
  7. 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.
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