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Title: Lattice Approximations of the First-Order Mean Field Type Differential Games
Authors: Averboukh, Y.
Issue Date: 2021
Publisher: Birkhauser
Springer Science and Business Media LLC
Citation: Averboukh Y. Lattice Approximations of the First-Order Mean Field Type Differential Games / Y. Averboukh // Nonlinear Differential Equations and Applications. — 2021. — Vol. 28. — Iss. 6. — 65.
Abstract: The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the approximations of the value function of the first-order mean field type differential game using solutions of model finite-dimensional differential games. The model game appears as a mean field type continuous-time Markov game, i.e., the game theoretical problem with the infinitely many agents and dynamics of each agent determined by a controlled finite state nonlinear Markov chain. Given a supersolution (resp. subsolution) of the Hamilton–Jacobi equation for the model game, we construct a suboptimal strategy of the first (resp. second) player and evaluate the approximation accuracy using the modulus of continuity of the reward function and the distance between the original and model games. This gives the approximations of the value function of the mean field type differential game by values of the finite-dimensional differential games. Furthermore, we present the way to build a finite-dimensional differential game that approximates the original game with a given accuracy. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85115247982
PURE ID: 23714244
ISSN: 1021-9722
metadata.dc.description.sponsorship: This work was funded by the Russian Science Foundation (Project No. 17-11-01093).
RSCF project card: 17-11-01093
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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