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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 3, Pages 299–308 (Mi vuu589)

MATHEMATICS

Randomized Nash equilibrium for differential games

Y. V. Averboukh

N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia

Abstract: The paper is concerned with the randomized Nash equilibrium for a nonzero-sum deterministic differential game of two players. We assume that each player is informed about the control of the partner realized up to the current moment. Therefore, the game is formalized in the class of randomized non-anticipative strategies. The main result of the paper is the characterization of a set of Nash values considered as pairs of expected players' outcomes. The characterization involves the value functions of the auxiliary zero-sum games. As a corollary we get that the set of Nash values in the case when the players use randomized strategies is a convex hull of the set of Nash values in the class of deterministic strategies. Additionally, we present an example showing that the randomized strategies can enhance the outcome of the players.

Keywords: differential games, Nash equilibrium, randomized strategies.

 Funding Agency Grant Number Russian Science Foundation 17-11-01093 This work was supported by the Russian Science Foundation (project no. 17-11-01093).

DOI: https://doi.org/10.20537/vm170301

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Document Type: Article
UDC: 517.977.8
MSC: 91A23, 91A10, 91A05
Language: English

Citation: Y. V. Averboukh, “Randomized Nash equilibrium for differential games”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:3 (2017), 299–308

Citation in format AMSBIB
\Bibitem{Ave17} \by Y.~V.~Averboukh \paper Randomized Nash equilibrium for differential games \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2017 \vol 27 \issue 3 \pages 299--308 \mathnet{http://mi.mathnet.ru/vuu589} \crossref{https://doi.org/10.20537/vm170301} \elib{http://elibrary.ru/item.asp?id=30267241}