Skip to main content
Log in

Pareto-Like Equilibria for Differential Games with Side Interests of the Players

  • Control Theory
  • Published:
Differential Equations Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

For dynamic and static problems with side interests of the participants, new concepts of conflict equilibrium are proposed, which make it possible to find a solution that most satisfies all the participants, especially in those problems in which all known concepts of equilibrium turn out to be ineffective or unsuitable.

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.

Similar content being viewed by others

References

  1. Isaacs, R., Differential Games, New York: Wiley, 1965.

    MATH  Google Scholar 

  2. McKinsey, J.C.C., Introduction to the Theory of Games, New York: McGraw-Hill, 1952.

    MATH  Google Scholar 

  3. Neumann, J. von and Morgenstern, O., Theory of Games and Economic Behavior, Princeton: Princeton Univ. Press, 1947.

    MATH  Google Scholar 

  4. Krasovskii, N.N. and Subbotin, A.I., Pozitsionnye differentsial’nye igry (Positional Differential Games), Moscow: Nauka, 1974.

    MATH  Google Scholar 

  5. Kurzhanskii, A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti (Control and Observation under Uncertainty), Moscow: Nauka, 1977.

    MATH  Google Scholar 

  6. Vaisbord, E.M. and Zhukovskii, V.I., Vvedenie v differentsial’nye igry neskol’kikh lits i ikh prilozheniya (Introduction to Multiperson Differential Games and Their Applications), Moscow: Sov. Radio, 1980.

    MATH  Google Scholar 

  7. Vorob’ev, N.N., Osnovy teorii igr: Beskoalitsionnye igry (Foundations of Game Theory: Noncooperative Games), Moscow: Nauka, 1984.

    MATH  Google Scholar 

  8. Chikrii, A.A., Konfliktno-upravlyaemye protsessy (Conflict-Controlled Processes), Kiev: Naukova Dumka, 1992.

    Google Scholar 

  9. Smol’yakov, E.R., Ravnovesnye modeli pri nesovpadayushchikh interesakh uchastnikov (Equilibrium Models with Noncoinciding Interests of the Participants), Moscow: Nauka, 1986.

    Google Scholar 

  10. Smol’yakov, E.R., Teoriya antagonizmov i differentsial’nye igry (Theory of Antagonisms and Differential Games), Moscow: Editorial URSS, 2000.

    Google Scholar 

  11. Smol’yakov, E.R., Teoriya konfliktnykh ravnovesii (Theory of Conflict Equilibria), Moscow: Editorial URSS, 2005.

    Google Scholar 

  12. Smol’yakov, E.R., Individual–Pareto equilibria for game problems with side interests of participants, Cybern. Syst. Anal., 2015, vol. 51, no. 2, pp. 187–197.

    Article  MathSciNet  MATH  Google Scholar 

  13. Smol’yakov, E.R., Upravlenie konfliktami s pobochnymi interesami uchastnikov (Control of Conflicts with Side Interests of the Participants), Saarbrücken: Lambert, 2013.

    Google Scholar 

  14. Smol’yakov, E.R., Theory of solution of differential games with side interests of the participants, Differ. Equations, 2014, vol. 50, no. 12, pp. 1650–1663.

    Article  MathSciNet  MATH  Google Scholar 

  15. Smol’yakov, E.R., Metody resheniya konfliktnykh zadach (Methods for Solving Conflict Problems), Moscow: Mosk. Gos. Univ., 2010.

    Google Scholar 

  16. Smol’yakov, E.R., Obobshchennoe optimal’noe upravlenie i dinamicheskie konfliktnye zadachi (Generalized Optimal Control and Dynamic Conflict Problems), Moscow: Mosk. Gos. Univ., 2010.

    Google Scholar 

  17. Smol’yakov, E.R., Conflict equilibria on sets with nonempty intersections, Dokl. Math., 2003, vol. 68, no. 1, pp. 42–45.

    MATH  Google Scholar 

  18. Smol’yakov, E.R., A theory of equilibria taking into account interests not related to conflicts, Dokl. Math., 2005, vol. 71, no. 3, pp. 476–479.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. R. Smol’yakov.

Additional information

Original Russian Text © E.R. Smol’yakov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 12, pp. 1703–1714.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Smol’yakov, E.R. Pareto-Like Equilibria for Differential Games with Side Interests of the Players. Diff Equat 53, 1654–1666 (2017). https://doi.org/10.1134/S0012266117120126

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266117120126

Navigation