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Weak Approachability

Author

Listed:
  • Nicolas Vieille

Abstract

In this paper, we study repeated games with vector payoffs. Following Blackwell [2], we define weak approachability and its dual property, weak excludability. We use results from differential games with fixed duration to prove that every set is either weakly approachable or weakly excludable.

Suggested Citation

  • Nicolas Vieille, 1992. "Weak Approachability," Post-Print hal-00481891, HAL.
    • Handle: RePEc:hal:journl:hal-00481891
    DOI: 10.1287/moor.17.4.781
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    Citations

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    Cited by:

    1. Dario Bauso & Hamidou Tembine & Tamer Başar, 2016. "Robust Mean Field Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 277-303, September.
    2. Fournier, Gaëtan & Kuperwasser, Eden & Munk, Orin & Solan, Eilon & Weinbaum, Avishay, 2021. "Approachability with constraints," European Journal of Operational Research, Elsevier, vol. 292(2), pages 687-695.
    3. Vianney Perchet, 2011. "Approachability of Convex Sets in Games with Partial Monitoring," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 665-677, June.
    4. Joseph M. Abdou & Nikolaos Pnevmatikos, 2019. "Asymptotic Value in Frequency-Dependent Games with Separable Payoffs: A Differential Approach," Dynamic Games and Applications, Springer, vol. 9(2), pages 295-313, June.
    5. Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information—The Limit Case," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 49-71, February.
    6. Sylvain Sorin, 2018. "Limit Value of Dynamic Zero-Sum Games with Vanishing Stage Duration," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 51-63, February.
    7. Ehud Lehrer & Eilon Solan, 2006. "Excludability and Bounded Computational Capacity," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 637-648, August.
    8. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
    9. 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.
    10. Rida Laraki, 2002. "Repeated Games with Lack of Information on One Side: The Dual Differential Approach," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 419-440, May.
    11. Rad Niazadeh & Negin Golrezaei & Joshua Wang & Fransisca Susan & Ashwinkumar Badanidiyuru, 2023. "Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization," Management Science, INFORMS, vol. 69(7), pages 3797-3817, July.

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