Coalition equilibrium in a three-person game

In this article, we suggest a new concept of an optimal solution in 3-person game, that we call “coalitional equilibrium”. This equilibrium based on the concepts of Nash and Berge equilibria obtained. We apply the concept of an optimal solution that cannot increase the outcome of a deviant coalition. Then we determine sufficient conditions of existence of a coalitional equilibrium using the Germeier resultant. These conditions can be reduced to building a saddle point in a special antagonistic game that can be effectively constructed on the mathematical model of the original game.