Anatolii F. Kleimenov     (N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620990; Ural Federal University, 19 Mira str., Ekaterinburg, 620002, Russian Federation)


An example of a non-antagonistic positional (feedback) differential two-person game (NPDG) is considered in which each of two players, in addition to the normal type of behavior, oriented toward maximizing own functional, can use other types of behavior. In particular, it can be altruistic and aggressive types. In the course of the game players can switch their behavior from one type to other. The use by players of types of behavior other than normal can lead to outcomes more preferable for them than in a game with only normal behavior. The example with the dynamics of simple motion on a plane and phase constraints illustrates the procedure of constructing new solutions.


Non-antagonistic positional differential game, Altruistic type of behavior, Agressive type of behavior

Full Text:



  1. Kleimenov A.F. Neantagonisticheskie positsionnye differentsialnye igry [Non-antagonistic Positional Differential Games]. Ekaterinburg: Nauka, 1993. 185 p. (in Russian).
  2. Kleimenov A.F. Solutions in a non-antagonistic positional differential game. J. Appl. Math. Mech., 1997. Vol. 61, No. 5. P. 717–723. DOI: 10.1016/S0021-8928(97)00094-4
  3. Kleimenov A.F. An approach to building dynamics for repeated bimatrix 2x2 games involving various behavior types. In: Dynamic and Control. London: Gordon and Breach Sci. Publ., 1998. P. 195–204.
  4. Kleimenov A.F. Altruistic behavior in a non-antagonistic positional differential game. Autom. Remote Control, 2017. Vol. 78, No. 4. P. 762–769. DOI: 10.1134/S0005117917040178
  5. Kleimenov A.F., Kryazhimskii A.V. Normal Behavior, Altruism and Aggression in Cooperative Game Dynamics. Interim Report IR-98-076. Laxenburg: IIASA, 1998. 47 p.
  6. Kononenko A.F. On equilibrium positional strategies in nonantagonistic differential games. Dokl. Akad. Nauk SSSR, 1976. Vol. 231, No. 2. P. 285–288. (in Russian).
  7. Krasovskii N.N. Upravlenie dinamicheskoi sistemoi [Control of a Dynamical System]. Moscow: Nauka, 1985. 520 p. (in Russian).
  8. Krasovskii N.N., Subbotin A.I. Game-Theoretical Control Problems. New York: Springer-Verlag, 1988. 517 p.
  9. Petrosyan L.A., Zenkevich N.A., Shevkoplyas E.V. Teoriya igr [Game Theory]. St. Petersburg: BHV-Petersburg, 2012. 424 p. (in Russian).


Article Metrics

Metrics Loading ...


  • There are currently no refbacks.