Abstract
In this paper, the results of the author’s previous work concerning a nonzero-sum positional differential game of two persons with different types of the players’ behavior are extended 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.
Similar content being viewed by others
REFERENCES
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974) [in Russian].
N. N. Krasovskii, Control of a Dynamical System (Nauka, Moscow, 1985) [in Russian].
L. A. Petrosyan, N. A. Zenkevich, and E. V. Shevkoplyas, Game Theory (BKhV-Peterburg, St. Petersburg, 2012) [in Russian].
A. F. Kleimenov, “Altruistic behavior in a nonantagonistic positional differential game,” Autom. Remote Control 78 (4), 762–769 (2017).
A. F. Kleimenov, “Aggressive behavior in a non-antagonistic positional differential game,” Autom. Remote Control 80 (1), 171–179 (2019).
A. F. Kleimenov, “Altruistic and aggressive types of behavior in a non-antagonistic positional differential two-person game,” IFAC-PapersOnLine 51 (32), 219–224 (2018).
A. F. Kleimenov, “On solutions in a nonantagonistic positional differential game,” J. Appl. Math. Mech. 61 (5), 717–723 (1997).
A. F. Kleimenov and A. V. Kryazhimskii, Normal Behavior, Altruism and Aggression in Cooperative Game Dynamics: IIASA Interim Report IR-98-076 (IIASA, Laxenburg, 1998).
A. F. Kleimenov, Nonzero-Sum Positional Differential Games (Nauka, Yekaterinburg, 1993) [in Russian].
A. F. Kleimenov, “An approach to building dynamics for repeated bimatrix 2 x 2 games involving various behavior types,” in Dynamic and Control, Ed. by G. Leitman et al. (Gordon and Breach, Amsterdam, 1999), pp. 195–204.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by I. Tselishcheva
Rights and permissions
About this article
Cite this article
Kleimenov, A.F. Altruistic and Aggressive Types of Behaviorin a Nonzero-Sum Positional Differential Gameof Three Persons. Proc. Steklov Inst. Math. 309 (Suppl 1), S74–S82 (2020). https://doi.org/10.1134/S0081543820040094
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543820040094