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Saddle points and active zero-sum equilibrium in games with multivalued functionals

  • Systems Analysis
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Cybernetics and Systems Analysis Aims and scope

Abstract

We consider existence and properties of saddle points of multivalued payoff functions on metric spaces and existence of active zero-sum equilibria which generalize the notion of saddle-point equilibrium. The results are applied to programmed zero-sum differential games.

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Literature Cited

  1. C. F. Roos, "Generalized Lagrange problems in the calculus of variations," Trans. AMS,30, 360–384 (1928).

    Google Scholar 

  2. J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, New York (1972).

    Google Scholar 

  3. N. N. Vorob'ev (ed.), Infinite Zero-Sum Games [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  4. N. Bourbaki, General Topology. Basic Structures [Russian translation], Nauka, Moscow (1968).

    Google Scholar 

  5. É. R. Smol'yakov, "Existence of solutions in zero-sum differential games," Kibernetika, No. 3, 96–99, 104 (1990).

    Google Scholar 

  6. É. R. Smol'yakov, Equilibrium Models for Players with Conflicting Interests [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  7. É. R. Smol'yakov, "’Active’ game equilibria in systems," in: Mathematical Methods in System Theory [in Russian], No. 6, VNIISI, Moscow (1980), pp. 31–51.

    Google Scholar 

  8. N. Bourbaki, General Topology. Topological Groups, Numbers, and Associated Groups in Space [Russian translation], Nauka, Moscow (1969).

    Google Scholar 

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Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 70–75, July–August, 1991.

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Smol'yakov, É.R. Saddle points and active zero-sum equilibrium in games with multivalued functionals. Cybern Syst Anal 27, 535–539 (1991). https://doi.org/10.1007/BF01130363

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  • DOI: https://doi.org/10.1007/BF01130363

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