A concept of nucleolus for uncertain coalitional game with application to profit allocation

Uncertain coalitional game is a type of coalitional games where the transferable payoffs are assumed to be uncertain variables. As solutions of uncertain coalitional game, uncertain core, uncertain Shapley value, and uncertain stable set have been offered. This article further presents a new thought of uncertain nucleolus as another solution to the uncertain coalitional game. Meantime, this paper proves that uncertain nucleolus is nonempty and singleton and proves that uncertain nucleolus is a subset of the uncertain core if the uncertain core is nonempty. Finally, an uncertain nucleolus is applied to resolve a profit allocation problem. (c) 2022 Elsevier Inc. All rights reserved.