Skip to main content
SpringerLink
Log in

Existence of Nash Equilibria for Linear Differential Games in Programmed Strategies

  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

We consider a linear differential game of N players described by a linear equation and establish a sufficient condition of the general form for the differential game guaranteeing the existence of at least one equilibrium point in Nash’s sense.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. I. Zhukovskii and M. E. Salukvadze, Some Game-Theoretical Control Problems and Their Applications [in Russian], Tbilisi (1998).

  2. A. F. Kleimenov, Nonzero Sum Positional Differential Games [in Russian], Ekaterinburg (1993).

  3. L. A. Petrosyan, N. A. Zenkevich, and E. A. Semina, Game Theory [in Russian], Moscow (1998).

  4. O. A. Malafeev, Controlled Conflict Systems [in Russian], Izd. St. Peterburg Univ. (2000).

  5. N. N. Vorob’ev, Elements of Game Theory. Coalitionless Games [in Russian], Moscow (1984).

  6. R. V. Gamkrelidze, Principles of Optimal Control [in Russian], Tbilisi (1977).

  7. J. Varga, Optimal Control of Differential and Functional Equations [Russian translation], Moscow (1977).

  8. L. Schwartz, Analysis [Russian translation], Vol. 1, Moscow (1972).

  9. H. Nikaido and K. Isoda, “Note on noncooperative convex games,” Pacific J. Math., Suppl., 1, pp. 807–815 (1955).

  10. N. T. Tynyanskii and V. I. Zhukovskii, “Nonzero sum differential games (coalitionless version),” in: Itogi Nauki i Tekhniki. Matematicheskii Analiz [in Russian], VINITI, Moscow, Vol. 15, pp. 199–266 (1977).

  11. E. R. Smol’yakov, Equilibrium Models with Players with Different Preferences [in Russian], Moscow (1986).

Download references

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, Faculty of Computation Mathematics and Cybernetics, Moscow, Russia

    M. S. Nikol’skii

Authors
  1. M. S. Nikol’skii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Problemy Dinamicheskogo Upravleniya, Issue 1, 2005, pp. 222–229.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nikol’skii, M.S. Existence of Nash Equilibria for Linear Differential Games in Programmed Strategies. Comput Math Model 25, 178–184 (2014). https://doi.org/10.1007/s10598-014-9218-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10598-014-9218-1

Keywords

Search

Navigation