Skip to main content
SpringerLink
Log in

Dynamical conflict models. I. Language of modeling

  • System Analysis and Operations Research
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

In this work, we present a novel paradigm for modeling and analysis of dynamical games and survey results that are most important from the point of view of this paradigm. We describe the basic qualitative characteristic features for solutions of dynamical games. The survey is primarily intended for mathematicians who use game theory in applied studies. We discuss the principles for choosing a language to describe dynamical conflicts.

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

  1. Vereshchagin, N.N. and Shen’, A., Yazyki i ischisleniya (Languages and Calculi), Moscow: Mosk. Tsentr Nepreryvnogo Mat. Obrazovaniya, 2012.

    Google Scholar 

  2. Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional’nogo analiza (Elements of the Theory of Functions and Functional Analysis), Moscow: Nauka, 1976.

    Google Scholar 

  3. Mal’tsev, A.I., Algoritmy i rekursivnye funktsii (Algorithms and Recursive Functions), Moscow: Nauka, 1986.

    Google Scholar 

  4. Uspenskii, V.A. and Semenov, A.L., Teoriya algoritmov: osnovnye otkrytiya i prilozheniya (Theory of Algorithms: Fundamental Discoveries and Applications), Moscow: Nauka, 1987.

    Google Scholar 

  5. Hausdorff, F., Grundzüge der Mengelehre, Leipzig: Veit, 1914. Translated under the title Teoriya mnozhestv, Moscow: ONTI, 1937.

    Google Scholar 

  6. Natanson, I.P., Teoriya funktsii veshchestvennoi peremennoi (Theory of Functions of a Real Variable), Moscow: Gostekhizdat, 1950.

    Google Scholar 

  7. Kanovei, V.G., Aksioma vybora i aksioma determinirovannosti (Axiom of Choice and Axiom of Determinacy), Moscow: Nauka, 1984.

    Google Scholar 

  8. Shibanov, A.S., Aleksandr Mikhailovich Lyapunov (Alexander Mikhaylovich Lyapunov), Moscow: Molodaya Gvardiya, 1985.

    Google Scholar 

  9. 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 

  10. Gardner, M., The Sixth Scientific American Book of Mathematical Puzzles and Diversions, New York: Simon & Schuster, 1971. Translated under the title Matematicheskie novelly, Moscow: Mir, 1974.

    Google Scholar 

  11. Berlekamp, E.R., Conway, J.H., and Guy, R.K., Winning Ways for Your Mathematical Plays, Wellesley: A.K. Peters, 2001, vol. 1; 2003, vol. 2; 2003, vol. 3; 2004, vol. 4.

    MATH  Google Scholar 

  12. Khagel’sbarger, D.U., SIIR—An Automaton for Extrapolating Sequences, in Kiberneticheskii Sb., no. 1, Moscow: Inostrannaya Literatura, 1960, pp. 275–289.

    Google Scholar 

  13. Gorelov, M.A., Three Etudes on Repeated Games, Upravlen. Bol’shimi Sist., 2008, no. 20, pp. 5–20.

    Google Scholar 

  14. Novikov, D.A. and Chkhartishvili, A.G., Refleksivnye igry (Reflexive Games), Moscow: Sinteg, 2003.

    Google Scholar 

  15. Neumann, J. and Morgenshtern, O., Theory of Games and Economic Behavior, Princeton: Princeton Univ. Press, 1953. Translated under the title Teoriya igr i ekonomicheskoe povedenie, Moscow: Nauka, 1970.

    MATH  Google Scholar 

  16. Kun, G.U., Extensive Games and the Problem of Information, in Pozitsionnye igry (Positional Games), Moscow: Nauka, 1967, pp. 13–40.

    Google Scholar 

  17. Berzh, K., A Set-Theoretic Approach to Sequential Games, in Pozitsionnye igry (Positional Games), Moscow: Nauka, 1967, pp. 155–182.

    Google Scholar 

  18. Kummer, B., Spiele auf Graphen, Berlin: Birkhäuser, 1980. Translated under the title Igry na grafakh, Moscow: Mir, 1982.

    Book  MATH  Google Scholar 

  19. Myerson, R.B., Game Theory: Analysis of Conflict, London: Harvard Univ. Press, 1997.

    Google Scholar 

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

    Google Scholar 

  21. Danil’chenko, T.N. and Kononenko, A.F., Dynamical Decision Making Models in Hierarchical Systems, in Sovremennoe sostoyanie teorii issledovaniya operatsii (Modern State of Operations Research), Moscow: Nauka, 1979, pp. 18–44.

    Google Scholar 

  22. 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 

  23. Isaaks, R., Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control, and Optimization, New York: Wiley, 1952. Translated under the title Differentsial’nye igry, Moscow: Mir, 1967.

    Google Scholar 

  24. Pontryagin, L.S., On the Theory of Differential Games, Usp. Mat. Nauk, 1966, vol. 21, no. 4, pp. 219–274.

    MATH  MathSciNet  Google Scholar 

  25. Pontryagin, L.S., Linear Differential Pursuit Games, Mat. Sb., 1980, vol. 112, no. 3, pp. 307–330.

    MathSciNet  Google Scholar 

  26. Krasovskii, N.N. and Subbotin, A.I., Pozitsionnye differentsial’nye igry (Positional Differential Games), Moscow: Nauka, 1974.

    MATH  Google Scholar 

  27. Subbotin, A.I. and Chentsov, N.N., Optimizatsiya garantii v zadachakh upravleniya (Guarantee Optimization in Control Problems), Moscow: Nauka, 1981.

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  29. Kononenko, A.F. and Shevchenko, V.V., Operatsionnye igry, teoriya i prilozheniya (Operational Games, Theory and Applications), Moscow: Vychisl. Tsentr Ross. Akad. Nauk, 2013.

    Google Scholar 

  30. Morozov, V.V., Sukharev, A.G., and Fedorov, V.V., Issledovanie operatsii v zadachakh i uprazhneniyakh (Operations Research in Problems and Exercises), Moscow: Vysshaya Shkola, 1986.

    Google Scholar 

  31. Bachet, de Meziriac, Problemes Plaisants et Delectables, qui se font par les Nombres, Lyon, 1612.

    Google Scholar 

  32. Mac Lane, S., Categories for the Working Mathematician, in Graduate Texts in Mathematics, New York: Springer, 1998, vol. 5. Translated under the title Kategorii dlya rabotayushchego matematika, Moscow: Fizmatlit, 2004.

    MATH  Google Scholar 

  33. Goldblatt, R., Topoi: The Categorial Analysis of Logic, New York: Dover, 1984. Translated under the title Toposy: kategornyi analiz logiki, Moscow: Mir, 1983.

    MATH  Google Scholar 

  34. Gorelov, M.A. and Kononenko, A.F., Informatsionnye aspekty prinyatiya reshenii v usloviyakh konflikta (Informational Aspects of Decision Making in Conflict Situations), Moscow: Vychisl. Tsentr Ross. Akad. Nauk, 1994.

    Google Scholar 

  35. Kukushkin, N.S. and Morozov, V.V., Teoriya neantagonisticheskikh igr (Theory of Non-Antagonistic Games), Moscow: Mosk. Gos. Univ., 1984.

    MATH  Google Scholar 

  36. Vatel’, I.A. and Ereshko, F.I., Matematika konflikta i sotrudnichestva (Mathematics of Conflict and Cooperation), Moscow: Znanie, 1973.

    Google Scholar 

  37. Zermelo, E., Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proc. Fifth Congress Mathematicians, (Cambridge 1912), Cambridge University Press, 1913, pp. 501–504. Translated as O primenenii teorii mnozhestv k teorii shakhmatnoi igry, in Matrichnye igry, Moscow: Nauka, 1961, pp. 167–172.

    Google Scholar 

  38. Pontryagin, L.S., Obyknovennye differentsial’nye uravneniya (Ordinary Differential Equations), Moscow: Nauka, 1982.

    MATH  Google Scholar 

  39. Propoi, A.I., Elementy teorii optimal’nykh diskretnykh protsessov (Elements of the Theory of Optimal Discrete Processes), Moscow: Nauka, 1973.

    Google Scholar 

  40. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., et al., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1969.

    Google Scholar 

  41. Moiseev, N.N., Elementy teorii optimal’nykh sistem (Elements of the Theory of Optimal Systems), Moscow: Nauka, 1975.

    Google Scholar 

  42. Kononenko, A.F., Structure of the Optimal Strategy in Dynamical Controllable Systems, Zh. Vychisl. Mat. Mat. Fiz., 1980, vol. 20, no. 5, pp. 1105–1116.

    MATH  MathSciNet  Google Scholar 

  43. 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 

  44. 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 

  45. Petrosyan, L.A., Zenkevich, N.A., and Shevkoplyas, E.V., Teoriya igr (Game Theory), St. Petersburg: BKhV-Peterburg, 2012.

    Google Scholar 

  46. Mazalov, V.V., Matematicheskaya teoriya igr i prilozheniya (Mathematical Game Theory and Applications), St. Petersburg: Lan’, 2010.

    Google Scholar 

  47. Kolokol’tsov, V.N. and Malafeev, O.A., Matematicheskoe modelirovanie mnogoagentnykh sistem konkurentsii i kooperatsii (Teoriya igr dlya vsekh) (Mathematical Modeling of Multiagent Systems of Competition and Cooperation (Game Theory for Everybody)), St. Petersburg: Lan’, 2012.

    Google Scholar 

  48. Dockner, E., Jorgensen, S., Long, N.V., et al., Differential Games in Economics and Management Science, Cambridge: Cambridge Univ. Press, 2000.

    Book  MATH  Google Scholar 

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

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, Russia

    M. A. Gorelov & A. F. Kononenko

Authors
  1. M. A. Gorelov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. F. Kononenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Gorelov.

Additional information

Original Russian Text © M.A. Gorelov, A.F. Kononenko, 2014, published in Avtomatika i Telemekhanika, 2014, No. 11, pp. 127–149.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gorelov, M.A., Kononenko, A.F. Dynamical conflict models. I. Language of modeling. Autom Remote Control 75, 1996–2013 (2014). https://doi.org/10.1134/S0005117914110083

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117914110083

Keywords

Search

Navigation