Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111400
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dc.contributor.authorAverboukh, Y.en
dc.date.accessioned2022-05-12T08:17:31Z-
dc.date.available2022-05-12T08:17:31Z-
dc.date.issued2021-
dc.identifier.citationAverboukh 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.en
dc.identifier.issn1021-9722-
dc.identifier.otherAll Open Access, Green3
dc.identifier.urihttp://hdl.handle.net/10995/111400-
dc.description.abstractThe 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.en
dc.description.sponsorshipThis work was funded by the Russian Science Foundation (Project No. 17-11-01093).en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.publisherBirkhauseren1
dc.publisherSpringer Science and Business Media LLCen
dc.relationinfo:eu-repo/grantAgreement/RSF//17-11-01093en
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceNonlinear Diff. Equ. Appl.2
dc.sourceNonlinear Differential Equations and Applicationsen
dc.subjectAPPROXIMATE SOLUTIONSen
dc.subjectEXTREMAL SHIFT RULEen
dc.subjectMEAN FIELD TYPE DIFFERENTIAL GAMESen
dc.subjectSUBOPTIMAL STRATEGIESen
dc.subjectVISCOSITY SOLUTIONSen
dc.titleLattice Approximations of the First-Order Mean Field Type Differential Gamesen
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/submittedVersionen
dc.identifier.scopus85115247982-
local.contributor.employeeAverboukh, Y., Krasovskii Institute of Mathematics and Mechanics UrB RAS, 16, S. Kovalevskoi str., Yekaterinburg, 620108, Russian Federation, Ural Federal University, 4, Turgeneva str., Yekaterinburg, 620075, Russian Federation, National Research University Higher School of Economics, Pokrovsky boulevard 11, Moscow, 109028, Russian Federationen
local.issue6-
local.volume28-
local.contributor.departmentKrasovskii Institute of Mathematics and Mechanics UrB RAS, 16, S. Kovalevskoi str., Yekaterinburg, 620108, Russian Federation; Ural Federal University, 4, Turgeneva str., Yekaterinburg, 620075, Russian Federation; National Research University Higher School of Economics, Pokrovsky boulevard 11, Moscow, 109028, Russian Federationen
local.identifier.pure23714244-
local.description.order65-
local.identifier.eid2-s2.0-85115247982-
local.fund.rsf17-11-01093-
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