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• W2738248110 abstract "In this paper, we explore Bertrand and Cournot Mean Field Games models for market competition with reflection boundary conditions. We prove existence, uniqueness and regularity of solutions to the system of equations, and show that this system can be written as an optimality condition of a convex minimization problem. We also provide a short proof of uniqueness to the system addressed in Graber and Bensoussan (Appl Math Optim 77:47–71, 2018), where uniqueness was only proved for small parameters 𝜖. Finally, we prove existence and uniqueness of weak solutions to the corresponding first order system at the deterministic limit." @default.
• W2738248110 created "2017-07-31" @default.
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• W2738248110 date "2018-01-01" @default.
• W2738248110 modified "2023-10-12" @default.
• W2738248110 title "Variational Mean Field Games for Market Competition" @default.
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• W2738248110 doi "https://doi.org/10.1007/978-3-030-01947-1_5" @default.
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