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Variational Time-Fractional Mean Field Games

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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.

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Acknowledgements

The first author would like to thank the hospitality of Università di Roma “La Sapienza” during preparation of this work. Qing Tang is partially supported by China National Science Foundation Grant No. 11701534. Both authors thank Mirko D’Ovidio (Università di Roma “La Sapienza”) for helpful discussions about fractional calculus and subordinated processes.

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Authors and Affiliations

  1. China University of Geosciences (Wuhan), Wuhan, China

    Qing Tang

  2. Università di Roma “La Sapienza”, Roma, Italy

    Fabio Camilli

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  1. Qing Tang
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  2. Fabio Camilli
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Correspondence to Fabio Camilli.

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Tang, Q., Camilli, F. Variational Time-Fractional Mean Field Games. Dyn Games Appl 10, 573–588 (2020). https://doi.org/10.1007/s13235-019-00330-2

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