Geodesic
Altruistic and Aggressive Types of Behavior in a Nonzero-Sum Positional Differential Game of Three Persons
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 3, pp. 108-117

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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.
Keywords: nonzero-sum positional differential game, terminal payoff functionals, altruistic and aggressive behavior types, Nash equilibrium solution. 
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     author = {A. F. Kleimenov},
     title = {Altruistic and {Aggressive} {Types} of {Behavior} in a {Nonzero-Sum} {Positional} {Differential} {Game} of {Three} {Persons}},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {108--117},
     publisher = {mathdoc},
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     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2019_25_3_a9/}
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A. F. Kleimenov. Altruistic and Aggressive Types of Behavior in a Nonzero-Sum Positional Differential Game of Three Persons. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 3, pp. 108-117. http://geodesic.mathdoc.fr/item/TIMM_2019_25_3_a9/