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Mat. Teor. Igr Pril., 2014, Volume 6, Issue 1, Pages 91–115 (Mi mgta129)  

This article is cited in 2 scientific papers (total in 2 papers)

On existence of $\varepsilon$-equilibrium in noncooperative $n$-person games associated with elliptic partial differential equations

Andrey V. Chernovab

a Nizhnii Novgorod State Technical University
b Nizhnii Novgorod State University

Abstract: The paper is devoted to obtaining the sufficient conditions for existence of the Nash $\varepsilon$-equilibrium in noncooperative $n$-person games associated with semilinear elliptic partial differential equations of the second order. Here, for all players, we consider only program strategies. The basis of the theory constructed consists in some assertion concerning the total preservation of solvability and the uniform solution boundedness of an operator equation of the first kind having been proved by the author formerly by means of a generalization of the method of monotone maps. As an auxiliary result of a specific interest we prove a theorem on convexity of the reachable set of a controlled semilinear elliptic equation.

Keywords: noncooperative $n$-person game, semilinear elliptic PDE of the second order, convexity of the reachable set, program strategies, $\varepsilon$-equilibrium.

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Citation: Andrey V. Chernov, “On existence of $\varepsilon$-equilibrium in noncooperative $n$-person games associated with elliptic partial differential equations”, Mat. Teor. Igr Pril., 6:1 (2014), 91–115

Citation in format AMSBIB
\Bibitem{Che14}
\by Andrey~V.~Chernov
\paper On existence of $\varepsilon$-equilibrium in noncooperative $n$-person games associated with elliptic partial differential equations
\jour Mat. Teor. Igr Pril.
\yr 2014
\vol 6
\issue 1
\pages 91--115
\mathnet{http://mi.mathnet.ru/mgta129}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Andrei V. Chernov, “O suschestvovanii ravnovesiya po Neshu v differentsialnoi igre, svyazannoi s ellipticheskimi uravneniyami: monotonnyi sluchai”, MTIP, 7:3 (2015), 48–78  mathnet
    2. A. V. Chernov, “Ob analoge teoremy Uintnera dlya upravlyaemogo ellipticheskogo uravneniya”, Izv. IMI UdGU, 2015, no. 2(46), 228–235  mathnet  elib
  • Математическая теория игр и её приложения
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