Skip to main content
Log in

Necessary and sufficient conditions for the existence of a saddle point in parametrized programmed differential games

  • Published:
Cybernetics and Systems Analysis Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. É. R. Smol'yakcn, “Differential games in mixed strategies,” Dokl. Akad. Nauk SSSR,191, No. 1, 39–41 (1970).

    Google Scholar 

  2. É. R. Smol'yakov, Equilibrium Models with Nonidentical Interests of the Players [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  3. N. N. Vorob'ev, Fundamentals of Game Theory. Coalitionless Games [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  4. G. A. Bliss, Lectures in Variational Calculus [Russian translation], IL, Moscow (1950).

    Google Scholar 

  5. R. J. Elliott, N. J. Kalton, and L. Markus, “Saddle points for linear differential games,” SI AM J. Contr.,11, No. 1, 100–112 (1973).

    Article  MATH  Google Scholar 

  6. N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  7. N. N. Krasovskii, Dynamic System Control. The Minmax Problem [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  8. É. R. Smol'yakov, “Existence of solutions in zero-sum differential games,” Kibernetika, No. 3, 96-99 (1990).

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

    Google Scholar 

  10. N. Dunford and J. Schwartz, Linear Operators. General Theory [Russian translation], IL, Moscow (1962).

    Google Scholar 

  11. E. R. Smol'yakov, “Saddle points and active zero-sum equilibrium in games with multivalued functional,” Kibern. Sist. Anal., No. 4, 70-75 (1991).

  12. O. A. Zhautykov, V. I. Zhukovskii, and S. Zharkynbaev, Many-Person Differential Games [in Russian], Nauka, Alma-Ata (1988).

    Google Scholar 

  13. Many-Person Differential Games. A Bibliography for 1968-1983 [in Russian], Russe, Bulgaria (1985).

    Google Scholar 

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

    Google Scholar 

  15. É. R. Smol'yakov, “Zero-sum equilibria,” Kibern. Sist. Anal., No. 6, 89-100 (1992).

  16. L. C. Young, Lectures on Calculus of Variations and Optimal Control Theory, Saunders, Philadelphia (1969).

    MATH  Google Scholar 

Download references

Authors

Additional information

Supported by the Russian Foundation of Basic Research, grant No. 95-01-00352.

Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 93–103, September–October, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smol’yakov, É.R. Necessary and sufficient conditions for the existence of a saddle point in parametrized programmed differential games. Cybern Syst Anal 33, 686–693 (1997). https://doi.org/10.1007/BF02667192

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02667192

Keywords

Navigation