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Approachability with constraints

Author

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  • Gaëtan Fournier

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Eden Kuperwasser

    (TAU - Tel Aviv University)

  • Orin Munk

    (TAU - Tel Aviv University)

  • Eilon Solan

    (TAU - Tel Aviv University)

  • Avishay Weinbaum

    (TAU - Tel Aviv University)

Abstract

We study approachability theory in the presence of constraints. Given a repeated game with vector payoffs, we study the pairs of sets (A, D) in the payoff space such that Player 1 can guarantee that the long-run average payoff converges to the set A, while the average payoff always remains in D. We provide a full characterization of these pairs when D is convex and open, and a sufficient condition when D is not convex.

Suggested Citation

  • Gaëtan Fournier & Eden Kuperwasser & Orin Munk & Eilon Solan & Avishay Weinbaum, 2021. "Approachability with constraints," Post-Print hal-03138536, HAL.
    • Handle: RePEc:hal:journl:hal-03138536
    DOI: 10.1016/j.ejor.2020.11.013
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03138536
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    References listed on IDEAS

    as
    1. Ehud Lehrer & Eilon Solan, 2016. "A General Internal Regret-Free Strategy," Dynamic Games and Applications, Springer, vol. 6(1), pages 112-138, March.
    2. Ehud Lehrer, 2004. "The Game of Normal Numbers," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 259-265, May.
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    4. Lehrer, Ehud & Solan, Eilon, 2009. "Approachability with bounded memory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 995-1004, July.
    5. Milman, Emanuel, 2006. "Approachable sets of vector payoffs in stochastic games," Games and Economic Behavior, Elsevier, vol. 56(1), pages 135-147, July.
    6. Xavier Spinat, 2002. "A Necessary and Sufficient Condition for Approachability," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 31-44, February.
    7. Flesch, János & Laraki, Rida & Perchet, Vianney, 2018. "Approachability of convex sets in generalized quitting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 411-431.
    8. Dario Bauso & Ehud Lehrer & Eilon Solan & Xavier Venel, 2015. "Attainability in Repeated Games with Vector Payoffs," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 739-755, March.
    9. Du, Ye & Lehrer, Ehud, 2020. "Constrained no-regret learning," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 16-24.
    10. Nicolas Vieille, 1992. "Weak Approachability," Post-Print hal-00481891, HAL.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    game theory; approachability; optimization;
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