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Home » Issues » Archive of Issues » 2017 - 3 issue » pp. 299-308

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Russia Yekaterinburg
Year
2017
Volume
27
Issue
3
Pages
299-308
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Section Mathematics
Title Randomized Nash equilibrium for differential games
Author(-s) Averboukh Yu.V.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa
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
UDC 517.977.8
MSC 91A23, 91A10, 91A05
DOI 10.20537/vm170301
Received 2 August 2017
Language English
Citation Averboukh Yu.V. Randomized Nash equilibrium for differential games, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 3, pp. 299-308.
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