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Sbornik: Mathematics, 2011, Volume 202, Issue 5, Pages 621–647
DOI: https://doi.org/10.1070/SM2011v202n05ABEH004158 (Mi sm7568) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Nash equilibrium in differential games and the construction of the programmed iteration method

Yu. V. Averboukh

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
English version PDF (416 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM2011v202n05ABEH004158
Abstract: This work is devoted to the study of nonzero-sum differential games. The set of payoffs in a situation of Nash equilibrium is examined. It is shown that the set of payoffs in a situation of Nash equilibrium coincides with the set of values of consistent functions which are fixed points of the program absorption operator. A condition for functions to be consistent is given in terms of the weak invariance of the graph of the functions under a certain differential inclusion.
Bibliography: 18 titles.
Keywords: differential games, Nash equilibrium, programmed iteration method.
Received: 07.04.2009 and 18.11.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 5, Pages 3–28
DOI: https://doi.org/10.4213/sm7568
Bibliographic databases:
Document Type: Article
UDC: 517.978.2
MSC: 49N70, 91A12
Language: English
Original paper language: Russian
Citation: Yu. V. Averboukh, “Nash equilibrium in differential games and the construction of the programmed iteration method”, Mat. Sb., 202:5 (2011), 3–28; Sb. Math., 202:5 (2011), 621–647
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:896
    Russian version PDF:212
    English version PDF:8
    References:70
    First page:40
     
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