A.F. Kleimenov. Аltruistic and aggressive types of behavior in a nonantagonistic positional differential game of three persons ... P. 108-117

In this paper, the results of the author's previous work concerning a nonantagonistic positional differential game of two persons with different types of the players' behavior are generalized to a game of three persons. For simplicity, the paradoxical type of behavior is not used by the players. The notions of altruistic and aggressive behavior types are generalized. As in the two-person game, it is assumed that each player chooses not only a positional strategy but also an indicator program function. The rules for forming controls for each triple of behavior types and the definition of a $BT$-solution are clarified. An example of a game with the dynamics of simple motion on a plane and a phase constraint is considered. It is assumed that the players can show altruism and aggression towards their partners, and the case of simultaneous aggression from all the players is not excluded. A description of $BT$-solutions of the game is given.

Keywords: nonantagonistic positional differential game, terminal payoff functionals, altruistic and aggressive behavior types, Nash equilibrium

Received May 16, 2019

Revised July 5, 2019

Accepted July 15, 2019

Anatolii Fedorovich Kleimenov, Dr. Phys.-Math. Sci., Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia; Ural Federal University, Yekaterinburg, 620083 Russia, e-mail: kleimenov@imm.uran.ru

REFERENCES

1.   Krasovskii N.N., Subbotin A.I. Game-theoretical control problems. N Y, Springer, 1988, 517 p. ISBN: 978-1-4612-8318-8. Original Russian text published in Krasovskii N.N., Subbotin A.I. Pozitsionnye differentsial’nye igry. Moscow: Nauka Publ., 1974, 456 p.

2.   Krasovskii N.N. Upravlenie dinamicheskoi sistemoi [Control of a dynamical system]. Moscow: Nauka Publ., 1985, 520 p.

3.   Petrosyan L.A., Zenkevich N.A., Shevkoplyas E.V. Teoriya igr [Game theory]. Saint Petersburg: BKhV-Peterburg Publ., 2012, 432 p. ISBN: 978-5-9775-0484-3 .

4.   Kleimenov A.F. Altruistic behavior in a nonantagonistic positional differential game. Autom. Remote Control, 2017, vol. 78, no. 4, pp. 762–769. doi: 10.1134/S0005117917040178 

5.   Kleimenov A.F. Aggressive behavior in a non-antagonistic positional differential game. Autom. Remote Control, 2019, vol. 80, no. 1, pp. 171–179. doi: 10.1134/S0005117919010156 

6.   Kleimenov, A.F. Altruistic and aggressive types of behavior in a non-antagonistic positional differential two-person game // IFAC-PapersOnLine. 2018. Vol. 51, iss 32. P. 219–224.

7.   Kleimenov A.F. On solutions in a nonantagonistic positional differential game. J. Appl. Math. Mech., 1997, vol. 61, no. 5, pp. 717–723. doi: 10.1016/S0021-8928(97)00094-4 

8.   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.

9.   Kleimenov, A.F. Nonantagonistic positional differential games (Neantagonisticheskie pozitsionnye differentsial’nye igry). Ekaterinburg: Nauka Publ., 1993, 185 p. ISBN: 5-7691-0353-1 .

10.   Kleimenov, A.F. An Approach to Building Dynamics for Repeated Bimatrix 2 × 2 Games Involving Various Behavior Types In: Dynamics and Control, Leitman G. etc (eds), London: Gordon and Breach, 1998, ISBN: 90-5699-172-8 , pp. 195–204.

Cite this article as: A.F. Kleimenov. Аltruistic and aggressive types of behavior in a nonantagonistic positional differential game of three persons, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 3, pp. 108–117.