Skip to main content
SpringerLink
Log in

Game theoretic formalization of the concept of sustainable development in the hierarchical control systems

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The resolution of numerous ecological problems on different levels must be implemented on the base of sustainable development concept that determines the conditions to the state of ecological-economic systems and impacting control actions. Those conditions can’t be realized by themselves and require special collaborative efforts of different agents using both cooperation and hierarchical control. To formalize the inevitable trade-offs it is natural to use game theoretic models. Unfortunately, the main optimality principles of hierarchical control (compulsion, impulsion) are not time consistent and therefore can’t be recommended as the direct base for collective solutions. The most prospective is the conviction method which is formalized as a transition from hierarchy to cooperation and allows a regularization that provides the time consistency. However, in current social conditions other methods of hierarchical control also keep their actuality. To ensure the time consistency of those optimality principles it is necessary to build cooperative differential games on their base. An example of the approach is considered in this paper.

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

  • Basar, T., & Olsder, G. J. (1995). Dynamic noncooperative game theory. San Diego: Academic Press.

    Google Scholar 

  • Denin, K. I., & Ugolnitsky, G. A. (2010). Game theoretic model of corruption in the systems of hierarchical control. Izvestia RAS: Teoria i Systemy Upravlenia (Journal of Computer and System Sciences International), 1, 192–198 (in Russian).

    Google Scholar 

  • Dockner, E. J., & Jorgensen, S. (1984). Cooperative and non-cooperative differential game solutions to an investment and pricing problem. The Journal of the Operational Research Society, 35, 731–739.

    Article  Google Scholar 

  • Dockner, E. J., & Long, N. V. (1993). International pollution control: cooperative versus non-cooperative strategies. Journal of Environmental Economics and Management, 24, 13–29.

    Article  Google Scholar 

  • French, J. P. R. Jr., & Raven, B. (1960). The bases of social power. In D. Cartwright & A. Zander (Eds.), Group dynamics (pp. 607–623). New York: Harper & Row.

    Google Scholar 

  • Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge: MIT Press.

    Google Scholar 

  • Gao, L., Jakubowski, A., Klompstra, M. B., & Olsder, G. J. (1989). Time-dependent cooperation in games. Berlin: Springer.

    Google Scholar 

  • Hamalainen, R. P., Haurie, A., & Kaitala, V. (1986). Equilibria and threats in a fishery management game. Optimal Control Applications & Methods, 6, 315–333.

    Article  Google Scholar 

  • Haurie, A. (1976). A note on nonzero-sum differential games with bargaining solutions. Journal of Optimization Theory and Applications, 18, 31–39.

    Article  Google Scholar 

  • Haurie, A. (1991). Piecewise deterministic and piecewise diffusion differential games with model uncertainties. Berlin: Springer.

    Google Scholar 

  • Haurie, A., & Pohjola, M. (1987). Efficient equilibria in a differential game of capitalism. Journal of Economic Dynamics & Control, 11, 65–78.

    Article  Google Scholar 

  • Haurie, A., & Zaccour, G. (1986). A differential game model of power exchange between interconnected utilizers. In Proceedings of the 25th IEEE conference on decision and control, Athens, Greece.

    Google Scholar 

  • Haurie, A., & Zaccour, G. (1991). A game programming approach to efficient management of interconnected power networks. Berlin: Springer.

    Google Scholar 

  • Haurie, A., Krawczyk, J. B., & Roche, M. (1994). Monitoring cooperative equilibria in a stochastic differential game. Journal of Optimization Theory and Applications, 81, 73–95.

    Article  Google Scholar 

  • Jorgensen, S., & Zaccour, G. (2001). Time consistent side payments in a dynamic game of downstream pollution. Journal of Economic Dynamics & Control, 25, 1973–1987.

    Article  Google Scholar 

  • Kaitala, V., & Pohjola, M. (1988). Optimal recovery of a shared resource stock: a differential game with efficient memory equilibria. Natural Resource Modeling, 3, 91–118.

    Google Scholar 

  • Kaitala, V., & Pohjola, M. (1995). Sustainable international agreements on greenhouse warming: a game theory study. Annals of the International Society of Dynamic Games, 2, 67–87.

    Google Scholar 

  • Kaitala, V., Maler, K. G., & Tulkens, H. (1995). The acid rain game as a resource allocation process with an application to the international cooperation among Finland, Russia, and Estonia. The Scandinavian Journal of Economics, 97, 325–343.

    Article  Google Scholar 

  • Kidland, F. E., & Prescott, E. C. (1977). Rules rather than decisions: the inconsistency of optimal plans. Journal of Political Economy, 85, 473–490.

    Article  Google Scholar 

  • Ledyaev, V. G. Power: a conceptual analysis. Nova Science Publishers, New York (1998).

    Google Scholar 

  • Leitmann, G. (1974). Cooperative and non-cooperative many players differential games. New York: Springer.

    Book  Google Scholar 

  • Leitmann, G. (1975) Cooperative and non-cooperative differential games. Amsterdam: Reidel.

    Google Scholar 

  • Maler, K. G., & de Zeeuw, A. D. (1998). The acid rain differential game. Environmental & Resource Economics, 12, 167–184.

    Article  Google Scholar 

  • Mazalov, V., & Rettieva, A. (2004). A fishery game model with migration: reserved territory approach. Game Theory and Applications, 10.

  • Mazalov, V., & Rettieva, A. (2005). Dynamic game methods for reserved territory optimization. Survey in Applied and Industrial Math., 3(12) (in Russian).

  • Mazalov, V., & Rettieva, A. (2006). Nash equilibrium in bioresource management problem. Mathematical Modeling, 5(18) (in Russian).

  • Mazalov, V., & Rettieva, A. (2007). Cooperative incentive equilibrium. In L. A. Petrosjan & N. A. Zenkevich (Eds.), Contributions to game theory and management. Collected papers presented on the international conference game theory and management. SPb, Graduate School of Management SPbU (pp. 316–325).

  • Ougolnitsky, G. A. (2002). Game theoretic modeling of the hierarchical control of sustainable development. In L. A. Petrosjan & V. V. Mazalov (Eds.), Game theory and applications (Vol. 8, pp. 82–91). New York: Nova Science Publishers.

    Google Scholar 

  • Ougolnitsky, G. A. (2009). A generalized model of hierarchically controlled dynamical system. In L. A. Petrosjan & N. A. Zenkevich (Eds.), Contributions to game theory and management. Vol. II. Collected papers presented on the second international conference game theory and management. SPb, Graduate School of Management SPbU (pp. 320–333).

  • Ougolnitsky, G. A., & Usov, A. B. (2009). Problems of the sustainable development of ecological-economic systems. In A. P. Cracknell, V. P. Krapivin, & C. A. Varotsos (Eds.), Global climatology and ecodynamics: anthropogenic changes to planet earth (pp. 427–444). Berlin: Springer-Praxis.

    Chapter  Google Scholar 

  • Petrosyan, L. A. (1977). The stability of solutions in differential games with many players. Vestnik Leningradskogo Universiteta, 1, 19(4), 46–52 (in Russian).

    Google Scholar 

  • Petrosyan, L. A. (1991). The time-consistency of the optimality principles in non-zero sum differential games. In R. P. Hamalainen & H. K. Ehtamo (Eds.), Lecture notes in control and information sciences (pp. 299–311). Berlin: Springer.

    Google Scholar 

  • Petrosyan, L. A. (1993b). Strongly time-consistent differential optimality principles. Vestnik Saint Petersburg University Mathematics, 26, 40–46 (in Russian).

    Google Scholar 

  • Petrosyan, L. A. (1993a). The time consistency in differential games with a discount factor. Game Theory and Applications, 1.

  • Petrosyan, L. A. (1997). Agreeable solutions in differential games. International Journal of Mathematics, Game Theory, and Algebra, 7, 165–177.

    Google Scholar 

  • Petrosyan, L. A., & Danilov, N. N. (1979). Stability of solutions in non-zero sum differential games with transferable payoffs. Vestnik of Leningrad University, 1, 52–59 (in Russian).

    Google Scholar 

  • Petrosyan, L. A., & Danilov, N. N. (1985). Cooperative differential games and their applications. Tomsk: Tomsk State University (in Russian).

    Google Scholar 

  • Petrosyan, L. A., & Zenkevich, N. A. (1996). Game theory. Singapore: World Scientific.

    Book  Google Scholar 

  • Petrosyan, L. A., & Zenkevich, N. A. (2007). Time consistency of cooperative solutions. In L. A. Petrosjan & N. A. Zenkevich (Eds.), Contributions to game theory and management. Collected papers presented on the international conference game theory and management. SPb, Graduate School of Management SBbU (pp. 413–440).

  • Petrosyan, L. A., & Zenkevich, N. A. (2009). Conditions for sustainable cooperation. In L. A. Petrosyan & N. A. Zenkevich (Eds.), Contributions to game theory and management. Vol. II. Collected papers presented on the second international conference game theory and management. SPb, Graduate School of Management SPbU (pp. 344–354).

  • Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mishchenko, E. F. (1962). The mathematical theory of optimal processes. New York: Wiley.

    Google Scholar 

  • Rubio, S. J., & Casino, B. (2002). A note on cooperative versus non-cooperative strategies in international pollution control. Resource and Energy Economics, 24, 251–261.

    Article  Google Scholar 

  • Rybasov, E. A., & Ugolnitsky, G. A. (2004). Mathematical modeling of the hierarchical control of ecological-economic systems considering corruption. In G. A. Ugolnitsky (Ed.), Computer modeling: ecology. iss. 2 (pp. 46–65). Moscow: Vuzovskaya Kniga (in Russian).

    Google Scholar 

  • Sorokin, P. (1957). Social and cultural dynamics. A study of change in major systems of art, truth, ethics, law and social relationships. Boston: Porter Sargent Publisher.

    Google Scholar 

  • Tahvonen, O. (1994). Carbon dioxide abatement as a differential game. European Journal of Political Economy, 10, 685–705.

    Article  Google Scholar 

  • Tolwinsky, B., Haurie, A., & Leitmann, G. (1986). Cooperative equilibria in differential games. Journal of Mathematical Analysis and Applications, 119, 182–202.

    Article  Google Scholar 

  • Ugolnitsky, G. A. (1999). Control of ecological-economic systems. Moscow: Vuzovskaya Kniga (in Russian).

    Google Scholar 

  • Ugolnitsky, G. A. (2002a). Game theoretic investigation of some methods of hierarchical control. Izvestia RAS: Teoria i Systemy Upravlenia (Journal of Computer and System Sciences International), 1, 97–101 (in Russian).

    Google Scholar 

  • Ugolnitsky, G. A. (2002b). Hierarchical control of the sustainable development of social organizations. Obshchestvennye Nauki i Sovremennost’ (Social Sciences and Modernity), 3, 133–140 (in Russian).

    Google Scholar 

  • Ugolnitsky, G. A. (2005). Game theoretic principles of optimality of the hierarchical control of sustainable development. Izvestia RAS: Teoria i Systemy Upravlenia (Journal of Computer and System Sciences International), 4, 72–78 (in Russian).

    Google Scholar 

  • Ugolnitsky, G. A., & Usov, A. B. (2007a). Mathematical formalization of the methods of hierarchical control of ecological-economic systems. Problemy Upravleniya (Control Problems), 4, 64–69 (in Russian).

    Google Scholar 

  • Ugolnitsky, G. A., & Usov, A. B. (2007b). Hierarchical systems of diamond-shaped structure for river water quality control. Upravlenie Bol’shimi Systemami (Control of Big Systems), 19, 187–203 (in Russian).

    Google Scholar 

  • Ugolnitsky, G. A., & Usov, A. B. (2008). An information-analytical system of control of the ecological-economic objects. Izvestia RAS: Teoria i Systemy Upravlenia (Journal of Computer and System Sciences International), 2, 168–176 (in Russian).

    Google Scholar 

  • Ugolnitsky, G. A., & Usov, A. B. (2009). Control of the complex ecological-economic systems. Avtomatika i Telemechanika (Automation and Remote Control), 5, 169–179 (in Russian).

    Google Scholar 

  • Uugolnitsky, G. A., & Usov, A. B. (2010). Three level fan-like systems of control of the ecological-economic objects. Problemy Upravleniya (Control Problems), 1, 26–32 (in Russian).

    Google Scholar 

  • United Nations, (1987). Report of the world commission on environment and development. General Assembly Resolution 42/187, 11 December.

  • Yeung, D. W. K. (2009). Cooperative game-theoretic mechanism design for optimal resource use. In L. A. Petrosyan & N. A. Zenkevich (Eds.), Contributions to game theory and management. Vol. II. Collected papers presented on the second international conference game theory and management. SPb, Graduate School of Management SPbU (pp. 483–513).

  • Yeung, D. W. K., & Petrosyan, L. A. (2001). Proportional time-consistent solution in differential games. Saint Petersburg: Saint Petersburg State University.

    Google Scholar 

Download references

Acknowledgements

The author thanks the two anonymous reviewers for very helpful comments and the Guest Editor David Yeung for his attention.

Author information

Authors and Affiliations

  1. Southern Federal University, 8A Milchakov St., 344090, Rostov-on-Don, Russia

    Guennady A. Ougolnitsky

Authors
  1. Guennady A. Ougolnitsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guennady A. Ougolnitsky.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ougolnitsky, G.A. Game theoretic formalization of the concept of sustainable development in the hierarchical control systems. Ann Oper Res 220, 69–86 (2014). https://doi.org/10.1007/s10479-012-1090-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-012-1090-9

Keywords

Search

Navigation