Skip to main content
Log in

Games with forbidden situations. Models with hard constraints

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

Abstract

We study and illustrate the techniques of modeling conflict situations when the capabilities of each side may depend on the actions of the partners. We consider conflicts where violating the constraints is physically impossible.

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. Vorob’ev, N.N., Teoriya igr dlya ekonomistov-kibernetikov (Game Theory for Economists-cyberneticians), Moscow, Nauka, 1985.

    Google Scholar 

  2. Owen, G., Game Theory, San Diego: Academic, 1995.

    Google Scholar 

  3. Germeier, Yu.B., Vvedenie v teoriyu issledovaniya operatsii (Introduction to Operation Research Theory), Moscow: Nauka, 1971.

    Google Scholar 

  4. Podinovskii, V.V. and Nogin, V.D., Pareto-optimal’nye resheniya mnogokriterial’nykh zadach (Pareto Optimal Solutions of Multicritea Problems), Moscow: Nauka, 1982.

    Google Scholar 

  5. Zermelo, E., Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proc. Fifth Int. Congr. Math., Cambridge, 1912, Cambridge: Cambridge Univ. Press, 1913, pp. 501–504. Translated under the title O primenenii teorii mnozhestv k teorii shakhmatnoi igry. Matrichnye igry, Moscow: Fizmatlit, 1961, pp. 167–172.

    Google Scholar 

  6. Neumann, J. von., Zur Theorie der Gesellschaftsspiele, Mathematische Annalen, 1928, vol. 100, pp. 295–320. Translated under the title K teorii strategicheskikh igr. Matrichnye igry, Moscow: Fizmatlit, 1961, pp. 173–204.

    Article  MATH  MathSciNet  Google Scholar 

  7. Kononenko, A.F. and Mukhtarov, U.M., Dinamicheskie sistemy s otvetstvennost’yu za vypolnenie svyazannykh ogranichenii (Dynamic Systems with Responsibility for Satisfying Dependent Constraints), Moscow: Vychisl. Tsentr Ross. Akad. Nauk, 2002.

    Google Scholar 

  8. Tokarev, V.V., Guaranteed Results in Games with Forbidden Situations, Autom. Remote Control, 2009, no. 6, pp. 1026–1042.

  9. Lagunov, V.N., A Multistep n-player Game with Phase Constraints, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1981, no. 4, pp. 19–24.

  10. Kukushkin, N.S. and Morozov, V.V., Teoriya neantagonisticheskikh igr (Non-antagonistic Game Theory), Moscow: Mosk. Gos. Univ., 1984.

    MATH  Google Scholar 

  11. Nash, J.F., The Bargaining Problem, Econometrica, 1950, vol. 18, no. 2, pp. 155–162.

    Article  MathSciNet  Google Scholar 

  12. Luce, R.D. and Raiffa, H., Games and Decisions: Introduction and Critical Survey, New York: Wiley, 1957. Translated under the title Igry i resheniya. Vvedenie i kriticheskii obzor, Moscow: Inostrannaya Literatuta, 1961.

    MATH  Google Scholar 

  13. Gorelov, M.A., Nikiforov, L.G., and Sokolov, V.P., Auktsiony GKO: ravnovesnoe reshenie (T-bills Auctions: The Equilibrium Solution), Rynok Tsennykh Bumag, 1997, no. 14, pp. 21–24; no. 15, pp. 4–9; no. 19, pp. 22–28.

  14. von Neumann, J. and Morgenstern, O., Theory of Games and Economic Behavior, Princeton: Princeton Univ. Press, 2007. Translated under the title Teoriya igr i ekonomicheskoe povedenie, Moscow: Nauka, 1970.

    MATH  Google Scholar 

  15. Burkov, V.N., Osnovy matematicheskoi teorii aktivnykh sistem (Fundamentals of the Mathematical Theory of Active Systems), Moscow: Nauka, 1977.

    Google Scholar 

  16. Kononenko, O.V., Mathematical Modeling of Economic Mechanisms for Interaction between Water Suppliers and Agricultural Companies), Vestn. S/Kh Nauki, 1981, no. 2, pp. 19–23.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © M.A. Gorelov, A.F. Kononenko, 2010, published in Avtomatika i Telemekhanika, 2010, No. 1, pp. 118–129.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gorelov, M.A., Kononenko, A.F. Games with forbidden situations. Models with hard constraints. Autom Remote Control 71, 105–115 (2010). https://doi.org/10.1134/S000511791001008X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S000511791001008X

Keywords

Navigation