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A zero-sum differential game for two opponent masses

Author

Listed:
  • Fabio Bagagiolo

    (University of Trento)

  • Rossana Capuani

    (University of Arizona)

  • Luciano Marzufero

    (Free University of Bozen-Bolzano)

Abstract

We investigate an infinite dimensional partial differential equation of Isaacs’ type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transport/continuity equation, where the control is given by the velocity vector field. Our study is set in the framework of the viscosity solutions theory in Hilbert spaces, and we prove the uniqueness of the value functions as solutions of the Isaacs equation.

Suggested Citation

  • Fabio Bagagiolo & Rossana Capuani & Luciano Marzufero, 2025. "A zero-sum differential game for two opponent masses," Partial Differential Equations and Applications, Springer, vol. 6(3), pages 1-23, June.
    • Handle: RePEc:spr:pardea:v:6:y:2025:i:3:d:10.1007_s42985-025-00322-5
    DOI: 10.1007/s42985-025-00322-5
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    References listed on IDEAS

    as
    1. Guofang Wang & Ziming Li & Wang Yao & Sikai Xia, 2022. "A Multi-Population Mean-Field Game Approach for Large-Scale Agents Cooperative Attack-Defense Evolution in High-Dimensional Environments," Mathematics, MDPI, vol. 10(21), pages 1-18, November.
    2. Diogo A. Gomes & João Saúde, 2021. "A Mean-Field Game Approach to Price Formation," Dynamic Games and Applications, Springer, vol. 11(1), pages 29-53, March.
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