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Finite composite games: Equilibria and dynamics

Author

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  • Sylvain Sorin

    (IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

  • Cheng Wan

    (Department of Economics, University of Oxford (UK) - Department of Economics, University of Oxford (UK))

Abstract

We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable players. We recall and compare the basic properties, expressed through variational inequalities, concerning equilibria, potential games and dissipative games, as well as evolutionary dynamics. Then we consider composite games where the three categories of participants are present, a typical example being congestion games, and extend the previous properties of equilibria and dynamics. Finally we describe an instance of composite potential game.

Suggested Citation

  • Sylvain Sorin & Cheng Wan, 2016. "Finite composite games: Equilibria and dynamics," Post-Print hal-02885860, HAL.
    • Handle: RePEc:hal:journl:hal-02885860
    DOI: 10.3934/jdg.2016005
    Note: View the original document on HAL open archive server: https://hal.science/hal-02885860
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    References listed on IDEAS

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    Cited by:

    1. Sylvain Sorin, 2023. "Continuous Time Learning Algorithms in Optimization and Game Theory," Dynamic Games and Applications, Springer, vol. 13(1), pages 3-24, March.
    2. Saeed Hadikhanloo & Rida Laraki & Panayotis Mertikopoulos & Sylvain Sorin, 2022. "Learning in nonatomic games, part Ⅰ: Finite action spaces and population games," Post-Print hal-03767995, HAL.
    3. Jacquot, Paulin & Wan, Cheng, 2022. "Nonatomic aggregative games with infinitely many types," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1149-1165.

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