Application of the altruistic and aggressive types of behavior in a two-person non-zero-sum positional differential game on the plane

A two-person non-zero-sum positional differential game is studied. In addition to the normal (nor) behavior aimed at maximizing the cost functional, each player can use other types of behavior, in particular, the altruistic (alt), aggressive (agg), and paradoxical (par) types. It is assumed that the players can switch between the types of behavior in the course of the game. Simultaneously with the choice of a positional strategy, each player also chooses an indicator function defined on the entire game interval and taking values in the set {nor, alt, agg, par}. The indicator function of each player shows the dynamics of behavior switchings of this player. The notion of $BT$-solution of the game is introduced. On $BT$-solutions, the application by a player of the behavior types different from normal produces a more favorable result for this player than a game with the normal behavior only. The procedure for constructing $BT$-solutions is exemplified by a planar game with simple motion dynamics and state constraints.