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Variational Time-Fractional Mean Field Games

Author

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  • Qing Tang

    (China University of Geosciences (Wuhan))

  • Fabio Camilli

    (Università di Roma “La Sapienza”)

Abstract

We consider the variational structure of a time-fractional second-order mean field games (MFG) system. The MFG system consists of time-fractional Fokker–Planck and Hamilton–Jacobi–Bellman equations. In such a situation, the individual agent follows a non-Markovian dynamics given by a subdiffusion process. Hence, the results of this paper extend the theory of variational MFG to the subdiffusive situation.

Suggested Citation

  • Qing Tang & Fabio Camilli, 2020. "Variational Time-Fractional Mean Field Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 573-588, June.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:2:d:10.1007_s13235-019-00330-2
    DOI: 10.1007/s13235-019-00330-2
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    References listed on IDEAS

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    1. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    2. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    3. Michael Benzaquen & Jean-Philippe Bouchaud, 2018. "A fractional reaction–diffusion description of supply and demand," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(2), pages 1-7, February.
    4. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    5. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    6. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    7. Michael Benzaquen & Jean-Philippe Bouchaud, 2018. "A fractional reaction–diffusion description of supply and demand," Post-Print hal-02323544, HAL.
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