COALITIONAL GAME WITH FUZZY PAYOFFS AND CREDIBILISTIC SHAPLEY VALUE

Abstract

Coalitional game deals with situations that involve cooperations among players, and there are different solution concepts such as the core, the Shapley value and the kernel. In many situations, there is no way to predict the payoff functions except for the expert experiences and subjective intuitions, which leads to the coalitional game with fuzzy payoffs. Within the framework of credibility theory, this paper employs two credibilistic approaches to define the behaviors of players under fuzzy situations. Correspondingly, two variations of Shapley value are proposed as the solutions of the coalitional game with fuzzy payoffs. Meanwhile, some characterizations of the credibilistic Shapley value are investigated. Finally, an example is provided for illustrating the usefulness of the theory developed in this paper.