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New Equilibria for Games with Side Interests of Participants*

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Abstract

Complicated concepts of equilibrium are given for static and dynamic conflict problems described by differential equations. The problems are considered both on a game set common to all participants and on partially overlapping game sets. The concepts are useful in searching for the strongest equilibrium in game problems and for determining a fair division of cooperative income.

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References

  1. R. Isaacs, Differential Games [Russian translation], Mir, Moscow (1967).

    MATH  Google Scholar 

  2. J. C. C. McKinsey, Introduction to the Theory of Games [Russian translation], Fizmatlit, Moscow (1960).

    MATH  Google Scholar 

  3. J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior [Russian translation], Nauka, Moscow (1970).

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    Google Scholar 

  9. E. R. Smol’yakov, Control of Conflicts with Side Interests of Participants, LAP LAMBERT Academic Publishing, Saarbrucken (2013).

    Google Scholar 

  10. E. R. Smol’yakov, “Theory of solution of differential games with side interests of participants,” Differential Equations, 50, No. 12, 1647–1659 (2014).

    MathSciNet  MATH  Google Scholar 

  11. E. R. Smol’yakov, “Individual and Pareto equilibria for game problems with side interests of participants,” Cybernetics and Systems Analysis, 51, No. 2, 29–41 (2015).

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  14. E. R. Smol’yakov, Methods for Solving Conflict Problems [in Russian], MGU, Moscow (2010).

    Google Scholar 

  15. E. R. Smol’yakov, Generalized Optimal Control and Dynamic Conflict Problems [in Russian], MGU, Moscow (2010).

    Google Scholar 

  16. E. R. Smol’yakov, Equilibrium Models with Noncoincident Interests of Participants [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  17. V. V. Podinovskii and V. D. Nogin, Pareto-Optimal Solutions of Multicriteria Problems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

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Correspondence to E. R. Smol’yakov.

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*This work was supported by the Russian Foundation for Basic Research, project No. 15-01-08838-a.

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2016, pp. 29–42.

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Smol’yakov, E.R. New Equilibria for Games with Side Interests of Participants* . Cybern Syst Anal 52, 524–535 (2016). https://doi.org/10.1007/s10559-016-9854-x

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  • DOI: https://doi.org/10.1007/s10559-016-9854-x

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