Skip to main content
SpringerLink
Log in

Strengthened equilibrium for game problems with side interest of participants

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

A strengthened equilibrium for conflict problems with partially overlapping game sets of participants is proposed, which is of substantial help in determining fair division in cooperative games and makes it possible to refine the hierarchy of all known equilibria.

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.

Similar content being viewed by others

References

  1. R. Isaacs, Differential Games (Wiley, New York, 1965; Mir, Moscow, 1967).

    MATH  Google Scholar 

  2. J. C. C. McKinsey, Introduction to the Theory of Games (McGraw-Hill, New York, 1952; Fizmatlit, Moscow, 1960).

    MATH  Google Scholar 

  3. J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, 2nd ed. (Princeton Univ. Press, Princeton, 1947).

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  5. A. B. Kurzhanovskii, Control and Observation in Uncertainty Conditions (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  6. E. M. Vaisbord and V. I. Zhukovskii, Introduction to Several-Person Differential Games and Their Applications (Sovetskoe Radio, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

  7. N. N. Vorob’ev, Foundations of Game Theory: Coalition-Free Games (Nauka, Moscow, 1984) [in Russian].

    Google Scholar 

  8. A. A. Chikrii, Conflict-Controlled Processes (Naukova Dumka, Kiev, 1992) [in Russian].

    MATH  Google Scholar 

  9. E. R. Smol’yakov, Dokl. Math. 68 (1), 42–45 (2003).

    Google Scholar 

  10. E. R. Smol’yakov, Dokl. Math. 93 (3), 251–255 (2016).

    Article  MathSciNet  Google Scholar 

  11. E. R. Smol’yakov, Kibernet. Syst. Anal., No. 3, 18–31 (2017).

    Google Scholar 

  12. E. R. Smol’yakov, Control of Conflicts with Side Interests of Participants (Lap Lambert Academic, Saarbrücken, 2013).

    Google Scholar 

  13. E. R. Smol’yakov, Theory of Antagonisms and Differential Games (Editorial URSS, Moscow, 2000) [in Russian].

    Google Scholar 

  14. E. R. Smol’yakov, Theory of Conflict Equilibria (Editorial URSS, Moscow, 2005) [in Russian].

    MATH  Google Scholar 

  15. E. R. Smol’yakov, Methods for Solving Conflict Problems (Izd. Mosk. Univ., Moscow, 2010) [in Russian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    E. R. Smol’yakov

Authors
  1. E. R. Smol’yakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. R. Smol’yakov.

Additional information

Original Russian Text © E.R. Smol’yakov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 474, No. 5, pp. 545–549.

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. Strengthened equilibrium for game problems with side interest of participants. Dokl. Math. 95, 259–263 (2017). https://doi.org/10.1134/S1064562417030206

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562417030206

Search

Navigation