Bargaining set, kernel and nucleolus for multi-choice games with coalition structure

In many actual application fields, solution concepts and their relationships in multi-choice games play important roles. For obtaining stable payoff vectors in multi-choice game, we extend several key solutions about bargaining set, kernel and nucleolus in classical cooperative game to multi-choice games with coalition structure, considering that multi-choice game is commonly with coalition structure. The extended bargaining set, kernel and nucleolus are generalizations to them in classical cooperative game. Furthermore, we deduce many relationships, that the kernel is a subset of the bargaining set, that the nucleolus is a subset of the kernel, that the nucleolus is existent and unique, and that the kernel and the bargaining set are existent.