Hybrid problem of dynamic control with three participants in the presence of altruistic and aggressive behavior types

The paper is close to [5] where a two-step hybrid dynamic control problem with three participants was considered; it was shown that in some cases it is profitable for the owner of management resources to sell a part of them to another participant(s) (assuming that the payoffs are transferable). This paper is also close to [4] where aggressive and altruistic types of behavior were allowed for the participants in three players differential game; then the players can apply the so-called $BT$-solutions which are better than the Nash ones. The developed in this paper approach is illustrated by a two-step control problem on a plane with the dynamics of simple motions in the presence of altruistic and aggressive behavior types.