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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2020, Volume 30, Issue 1, Pages 3–17 (Mi vuu706)  

MATHEMATICS

Markov approximations of nonzero-sum differential games

Yu. V. Averboukhab

a Krasovskii Institute of Mathematics and Mechanics, 16, ul. S. Kovalevskoi, Yekaterinburg, 620219, Russia
b Institute of Natural Sciences and Mathematics, Ural Federal University, ul. Turgeneva, 4, Yekaterinburg, 620000, Russia

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.

Funding Agency Grant Number
Russian Science Foundation 17-11-01093
This work was funded by the Russian Science Foundation (Project No. 17-11-01093).


DOI: https://doi.org/10.35634/vm200101

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Full text: http://vm.udsu.ru/.../2020-1-1
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Bibliographic databases:

UDC: 517.977.8
MSC: 91A23, 91A10, 91A05
Received: 17.11.2019
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Citation: Yu. V. Averboukh, “Markov approximations of nonzero-sum differential games”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:1 (2020), 3–17

Citation in format AMSBIB
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\by Yu.~V.~Averboukh
\paper Markov approximations of nonzero-sum differential games
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 1
\pages 3--17
\mathnet{http://mi.mathnet.ru/vuu706}
\crossref{https://doi.org/10.35634/vm200101}
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