Hybrid equilibrium in $N$-person games

How can we combine altruism of Berge equilibrium with selfishness of Nash equilibrium? The positive answer to this question will be given below. In short, they can be combined but in the class of mixed strategies. For a noncooperative $N$-player normal form game, we introduce the concept of hybrid equilibrium (HE) by synthesizing the concepts of Nash and Berge equilibria and Pareto maximum. Some properties of this equilibrium are explored and its existence in mixed strategies is established under standard assumptions of mathematical game theory (convex and compact strategy sets and continuous payoff functions).