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Infinite Histories and Steady Orbits in Repeated Games

Author

Listed:
  • Itzhak Gilboa

    () (Northwestern University [Evanston])

  • David Schmeidler

    (Tel Aviv University [Tel Aviv], OSU - Ohio State University [Columbus])

Abstract

We study a model of repeated games with the following features: (a) Infinite histories. The game has been played since days of yore, or is so perceived by the players: (b) Turing machines with memory. Since regular Turing machines coincide with bounded recall strategies (in the presence of infinite histories), we endow them with "external" memory; (c) Nonstrategic players. The players ignore complicated strategic considerations and speculations about them. Instead, each player uses his/her machine to update some statistics regarding the others′ behaviour, and chooses a best response to observed behaviour. Relying on these assumptions, we define a solution concept for the one shot game, called steady orbit. The (closure of the) set of steady orbit payoffs strictly includes the convex hull of the Nash equilibria payoffs and is strictly included in the correlated equilibria payoffs. Assumptions (a)-(c) above are independent to a large extent. In particular, one may define steady orbits without explicitly dealing with histories or machines.

Suggested Citation

  • Itzhak Gilboa & David Schmeidler, 1994. "Infinite Histories and Steady Orbits in Repeated Games," Post-Print hal-00481357, HAL.
  • Handle: RePEc:hal:journl:hal-00481357
    DOI: 10.1006/game.1994.1022
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00481357
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    Cited by:

    1. Bavly, Gilad & Neyman, Abraham, 2014. "Online concealed correlation and bounded rationality," Games and Economic Behavior, Elsevier, vol. 88(C), pages 71-89.

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    Keywords

    game; repeated game; model;

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