Uncertain Shapley value of coalitional game with application to supply chain alliance

Uncertain coalitional game deals with situations in which the transferable payoffs are uncertain variables. The uncertain core has been proposed as the solution of uncertain coalitional game. This paper goes further by presenting two definitions of uncertain Shapley value: expected Shapley value and ̨-optimistic Shapley value. Meanwhile, some characterizations of the uncertain Shapley value are investigated. Finally, vailable online 27 June 2016 eywords: oalitional game ncertain payoff hapley value as an application, uncertain Shapley value is used to solve a profit allocation problem of supply chain alliance. © 2016 Elsevier B.V. All rights reserved. upply chain alliance