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Repetition and cooperation: A model of finitely repeated games with objective ambiguity

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  • Demeze-Jouatsa, Ghislain-Herman

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper, we present a model of finitely repeated games in which players can strategically make use of objective ambiguity. In each round of a finite rep- etition of a finite stage-game, in addition to the classic pure and mixed actions, players can employ objectively ambiguous actions by using imprecise probabilistic devices such as Ellsberg urns to conceal their intentions. We find that adding an infinitesimal level of ambiguity can be enough to approximate collusive payoffs via subgame perfect equi- librium strategies of the finitely repeated game. Our main theorem states that if each player has many continuation equilibrium payoffs in ambiguous actions, any feasible pay- off vector of the original stage-game that dominates the mixed strategy maxmin payoff vector is (ex-ante and ex-post) approachable by means of subgame perfect equilibrium strategies of the finitely repeated game with discounting. Our condition is also necessary.

Suggested Citation

  • Demeze-Jouatsa, Ghislain-Herman, 2018. "Repetition and cooperation: A model of finitely repeated games with objective ambiguity," Center for Mathematical Economics Working Papers 585, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:585
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    File URL: https://pub.uni-bielefeld.de/download/2930384/2930385
    File Function: First Version, 2018
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    References listed on IDEAS

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    2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
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    4. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    5. Wen, Quan, 1994. "The "Folk Theorem" for Repeated Games with Complete Information," Econometrica, Econometric Society, vol. 62(4), pages 949-954, July.
    6. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    7. Joseph Greenberg, 2000. "The Right to Remain Silent," Theory and Decision, Springer, vol. 48(2), pages 193-204, March.
    8. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-948, July.
    9. Sekiguchi, Tadashi, 2002. "Existence of nontrivial equilibria in repeated games with imperfect private monitoring," Games and Economic Behavior, Elsevier, vol. 40(2), pages 299-321, August.
    10. Sibly, Hugh & Tisdell, John, 2018. "Cooperation and turn taking in finitely-repeated prisoners' dilemmas: An experimental analysis," Journal of Economic Psychology, Elsevier, vol. 64(C), pages 49-56.
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    Keywords

    Objective Ambiguity; Ambiguity Aversion; Finitely Repeated Games; Subgame Perfect Equilibrium; Ellsberg Urns; Ellsberg Strategies;

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