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Correlation through Bounded Recall Strategies

  • Ron Peretz
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    Two agents independently choose mixed m-recall strategies that take actions in finite action spaces A1 and A2. The strategies induce a random play, a1,a2,..., where at assumes values in A1 X A2. An M-recall observer observes the play. The goal of the agents is to make the observer believe that the play is similar to a sequence of i.i.d. random actions whose distribution is Q \in \Delta(A1 X A2). For nearly every t, the following event should occur with probability close to one: "the distribution of a_{t+M} given at a_t,..,a_{t+M} is close to Q." We provide a sufficient and necessary condition on m, M, and Q under which this goal can be achieved (for large m). This work is a step in the direction of establishing a folk theorem for repeated games with bounded recall. It tries to tackle the difficulty in computing the individually rational levels (IRL) in the bounded recall setting. Our result implies, for example, that in some games the IRL in the bounded recall game is bounded away below the IRL in the stage game, even when all the players have the same recall capacity.

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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp579.pdf
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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 dp579.

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    Length: 21 pages
    Date of creation: 21 Jul 2011
    Date of revision:
    Handle: RePEc:huj:dispap:dp579
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    1. Abraham Neyman & Joel Spencer, 2006. "Complexity and Effective Prediction," Discussion Paper Series dp435, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Neyman, Abraham & Okada, Daijiro, 2009. "Growth of strategy sets, entropy, and nonstationary bounded recall," Games and Economic Behavior, Elsevier, vol. 66(1), pages 404-425, May.
    3. 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.
    4. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
    5. Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Levine's Working Paper Archive 122247000000002427, David K. Levine.
    6. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
    7. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
    8. 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.
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