On one hybrid equilibrium

The notion of $BN$-hybrid equilibrium is proposed for a noncooperative $N$-person game. It is assumed that each player belongs to one of two classes: altruists and pragmatists. The altruists and the pragmatists choose their strategies using the concepts of the Berge equilibrium and the Nash equilibrium, respectively. Using a specially constructed Germeier convolution based on payoff functions, we obtain sufficient conditions for the existence of a $BN$-hybrid equilibrium. For an extension of the game with mixed strategies, a theorem on the existence of a $BN$-hybrid equilibrium is proved under constraints standard for mathematical game theory, namely, under the assumptions that the sets of the players' strategies are convex and compact and their payoff functions are continuous. The proposed concept is extended to noncooperative $N$-person games under interval uncertainty. An existence theorem is given for a strongly guaranteed $N$-hybrid equilibrium in mixed strategies.