Section
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Mathematics
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Title
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Markov approximations of nonzero-sum differential games
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Author(-s)
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Averboukh Yu.V.ab
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Affiliations
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Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa,
Ural Federal Universityb
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Abstract
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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.
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Keywords
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nonzero-sum differential games, approximate Nash equilibria, Markov games, differential inclusion
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UDC
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517.977.8
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MSC
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91A23, 91A10, 91A05
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DOI
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10.35634/vm200101
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Received
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17 November 2019
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Language
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English
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Citation
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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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References
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