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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 with local coupling. 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, providing an Eulerian interpretation of time-fractional MFG systems.

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      The random walk's guide to anomalous diffusion: a fractional dynamics approach

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        Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

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          Mean field games

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            Author and article information

            Journal
            13 December 2018
            1812.05431

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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            math.AP

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