Existence and non-existence for time-dependent mean field games with\n strong aggregation

2020/11/02 by Marco Cirant, Cirant, Marco, Daria Ghilli +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Mathematics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2011.00798

openalex publication_date 2020/11/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We investigate the existence of classical solutions to second-order quadratic\nMean-Field Games systems with local and strongly decreasing couplings of the\nform -\σ m^\α, \α \≥ 2/N, where m is the population density\nand N is the dimension of the state space. We prove the existence of\nsolutions under the assumption that \σ is small enough. For large\n\σ, we show that existence may fail whenever the time horizon T is\nlarge.\n

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• The local Turnpike Property in Mean Field Control and Games with quadratic Hamiltonian
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