Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/101551
Title: Deterministic Limit of Mean Field Games Associated with Nonlinear Markov Processes
Authors: Averboukh, Y.
Issue Date: 2020
Publisher: Springer
Citation: Averboukh Y. Deterministic Limit of Mean Field Games Associated with Nonlinear Markov Processes / Y. Averboukh. — DOI 10.1007/s00245-018-9486-9 // Applied Mathematics and Optimization. — 2020. — Vol. 81. — Iss. 3. — P. 711-738.
Abstract: The paper is concerned with the deterministic limit of mean field games with a nonlocal coupling. It is assumed that the dynamics of mean field games are given by nonlinear Markov processes. This type of games includes stochastic mean field games as well as mean field games with finite state space. We consider the limiting deterministic mean field game within the framework of minimax approach. The concept of minimax solutions is close to the probabilistic formulation. In this case the Hamilton–Jacobi equation is considered in the minimax/viscosity sense, whereas the flow of probabilities is determined by the probability on the set of solutions of the differential inclusion associated with the Hamilton–Jacobi equation such that those solutions are viable in the graph of the minimax solution. The main result of the paper is the convergence (up to subsequence) of the solutions of the mean field games to the minimax solution of a deterministic mean field game in the case when the underlying dynamics converge to the deterministic evolution. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords: DETERMINISTIC LIMIT
MEAN FIELD GAMES
MINIMAX SOLUTIONS
FLOW GRAPHS
STOCHASTIC SYSTEMS
DETERMINISTIC LIMIT
DIFFERENTIAL INCLUSIONS
FINITE STATE SPACES
MEAN FIELD GAMES
MINIMAX
NONLOCAL COUPLING
PROBABILISTIC FORMULATION
UNDERLYING DYNAMICS
MARKOV PROCESSES
URI: http://hdl.handle.net/10995/101551
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85081402595
PURE ID: 13142324
fbb4fb1c-331e-477d-ad8f-1440392bdc1b
ISSN: 954616
DOI: 10.1007/s00245-018-9486-9
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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