Skip to main content
Log in

Equilibria in models of hierarchically organized dynamical control systems with regard to sustainable development conditions

  • Control in Social Economic Systems, Medicine, and Biology
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We study dynamic game theoretic models for two- and three-level control systems taking into account sustainable development conditions. We consider methods of compulsion and impulsion as hierarchical control methods. We give definitions of equilibria and show algorithms for constructing them in various cases.

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. Von Stackelberg, H., Marktform und Gleichgewicht, Vienna: Springer-Verlag, 1934.

    Google Scholar 

  2. Basar, T. and Olsder, G.J., Dynamic Noncooperative Game Theory, SIAM: Philadelphia, 1999.

    MATH  Google Scholar 

  3. Dockner, E., Jorgensen, S., Long, N.V., and Sorger, G., Differential Games in Economics and Management Science, Cambridge: Cambridge Univ. Press, 2000.

    Book  MATH  Google Scholar 

  4. Jorgensen, S. and Zaccour, G., Differential Games in Marketing, New York: Springer, 2004.

    Book  Google Scholar 

  5. Laffont, J.-J. and Martimort, D., The Theory of Incentives: The Principal-Agent Model, Princeton: Princeton Univ. Press, 2002.

    Google Scholar 

  6. Germeier, Yu.B., Igry s neprotivopolozhnymi interesami (Games with Non-Antagonistic Interests), Moscow: Nauka, 1976.

    Google Scholar 

  7. Gorelik, V.A. and Kononenko, A.F., Teoretiko-igrovye modeli prinyatiya reshenii v ekologo-ekonomicheskikh sistemakh (Game Theoretic Decision Making Models in Ecological-Economical Systems), Moscow: Radio i Svyaz’, 1982.

    Google Scholar 

  8. Gorelik, V.A., Gorelov, M.A., and Kononenko, A.F., Analiz konfliktnykh situatsii v sistemakh upravleniya (Analyzing Conflict Situations in Control Systems), Moscow: Radio i Svyaz’, 1991.

    Google Scholar 

  9. Kononenko, A.F., Khalezov, A.D., and Chumakov, V.V., Prinyatie reshenii v usloviyakh neopredelennosti (Decision Making under Uncertainty), Moscow: Vychisl. Tsentr Akad. Nauk SSSR, 1991.

    Google Scholar 

  10. Gorelov, M.A. and Kononenko, A.F., Games with Forbidden Situations. Models with Hard Constraints, Autom. Remote Control, 2010, vol. 71, no. 1, pp. 105–115.

    Article  MATH  MathSciNet  Google Scholar 

  11. Gorelov, M.A. and Kononenko, A.F., Games with Forbidden Situations. Models with Soft Constraints, Autom. Remote Control, 2010, vol. 71, no. 5, pp. 826–836.

    Article  MATH  MathSciNet  Google Scholar 

  12. Burkov, V.N. and Novikov, D.A., Teoriya aktivnykh sistem: sostoyanie i perspektivy (Theory of Active Systems: State of Affairs and Future Prospects), Moscow: Sinteg, 1999.

    Google Scholar 

  13. Novikov, D.A., Teoriya upravleniya organizatsionnymi sistemami (Control Theory for Organizational Systems), Moscow: Mosk. Psikhol.-Sotsial. Inst., 2005.

    Google Scholar 

  14. Novikov, D.A. and Chkhartishvili, A.G., Refleksiya i upravlenie: matematicheskie modeli (Reflexivity and Control: Mathematical Models), Moscow: Fizmatlit, 2013.

    Google Scholar 

  15. Petrosyan, L.A. and Shiryaev, V.D., Ierarkhicheskie igry (Hierarchical Games), Saransk: Mordov. Univ., 1986.

    MATH  Google Scholar 

  16. Petrosyan, L.A. and Zakharov, V.V., Vvedenie v matematicheskuyu ekologiyu (Introduction to Mathematical Ecology), Leningrad: Leningr. Gos. Univ., 1986.

    Google Scholar 

  17. Petrosyan, L.A. and Tomskii, G.V., Dinamicheskie igry i ikh prilozheniya (Dynamical Games and Their Applications), Leningrad: Leningr. Gos. Univ., 1982.

    MATH  Google Scholar 

  18. Petrosyan, L.A. and Kuzyutin, D.V., Ustoichivye resheniya pozitsionnykh igr (Stable Solutions of Positional Games), St. Petersburg: S.-Peterburg. Gos. Univ., 2008.

    Google Scholar 

  19. Zenkevich, N.A., Petrosyan, L.A., and Yang, D.V.K., Dinamicheskie igry i ikh prilozheniya v menedzhmente (Dynamical Games and Their Applications in Management), St. Petersburg: Vysshaya Shkola Menedzhmenta, 2009.

    Google Scholar 

  20. Ugol’nitskii, G.A., Ierarkhicheskoe upravlenie ustoichivym razvitiem (Hierarchical Control over Sustainable Development), Moscow: Fizmatlit, 2010.

    Google Scholar 

  21. Ugol’nitskii, G.A., Ustoichivoe razvitie organizatsii (Sustainable Development of Organizations), Moscow: Fizmatlit, 2011.

    Google Scholar 

  22. Moulin, H., Game Theory for the Social Sciences (Studies in Game Theory and Mathematical Economics), New York: New York Univ. Press, 1982. Translated under the title Teoriya igr s primerami iz matematicheskoi ekonomiki, Moscow: Mir, 1985.

    MATH  Google Scholar 

  23. Ugol’nitskii, G.A., Game-Theoretic Optimality Principles for Hierarchical Control over Sustainable Development, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2005, no. 4, pp. 72–78.

    Google Scholar 

  24. Ugol’nitskii, G.A., A Game-Theoretic Study of Some Methods of Hierarchical Control, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2002, no. 1, pp. 97–101.

    Google Scholar 

  25. Kononenko, A.F., On Multistep Conflicts with Information Exchange, Zh. Vychisl. Mat. Mat. Fiz., 1977, no. 4, pp. 922–931.

    Google Scholar 

  26. Ugol’nitskii, G.A. and Usov, A.B., A Study of Differential Models for Hierarchical Control System via Their Discretization, Autom. Remote Control, 2010, vol. 74, no. 2, pp. 252–263.

    Article  Google Scholar 

  27. Ugol’nitskii, G.A. and Usov, A.B., Three-Level Control Systems for Ecological-Economical Objects of Fan-like Structure, Probl. Upravlen., 2010, no. 1, pp. 26–32.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. A. Ugol’nitskii.

Additional information

Original Russian Text © G.A. Ugol’nitskii, A.B. Usov, 2014, published in Avtomatika i Telemekhanika, 2014, No. 6, pp. 86–102.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ugol’nitskii, G.A., Usov, A.B. Equilibria in models of hierarchically organized dynamical control systems with regard to sustainable development conditions. Autom Remote Control 75, 1055–1068 (2014). https://doi.org/10.1134/S000511791406006X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000511791406006X

Keywords

Navigation