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Russia Yekaterinburg
Section Mathematics
Title Markov approximations of nonzero-sum differential games
Author(-s) Averboukh Yu.V.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract The paper is concerned with approximate solutions of nonzero-sum differential games. An approximate Nash equilibrium can be designed by a given solution of an auxiliary continuous-time dynamic game. We consider the case when dynamics is determined by a Markov chain. For this game the value function is determined by an ordinary differential inclusion. Thus, we obtain a construction of approximate equilibria with the players' outcome close to the solution of the differential inclusion. Additionally, we propose a way of designing a continuous-time Markov game approximating the original dynamics.
Keywords nonzero-sum differential games, approximate Nash equilibria, Markov games, differential inclusion
UDC 517.977.8
MSC 91A23, 91A10, 91A05
DOI 10.35634/vm200101
Received 17 November 2019
Language English
Citation Averboukh Yu.V. Markov approximations of nonzero-sum differential games, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 1, pp. 3-17.
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