Short-Time Existence for a General Backward–Forward Parabolic System Arising from Mean-Field Games

Marco Cirant (), Roberto Gianni () and Paola Mannucci ()
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Marco Cirant: Università di Padova
Roberto Gianni: Università di Firenze
Paola Mannucci: Università di Padova

Dynamic Games and Applications, 2020, vol. 10, issue 1, No 5, 100-119

Abstract: Abstract We study the local in time existence of a regular solution of a nonlinear parabolic backward–forward system arising from the theory of mean-field games (briefly MFG). The proof is based on a contraction argument in a suitable space that takes account of the peculiar structure of the system, which involves also a coupling at the final horizon. We apply the result to obtain existence to very general MFG models, including also congestion problems.

Keywords: Parabolic equations; Backward–forward system; Mean-field games; Hamilton–Jacobi; Fokker–Planck; Congestion problems; 35K40; 35K61; 49N90 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13235-019-00311-5

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