Grey Sharpley model and its Raiffa solution for benefit allocation in cooperative game

In this paper a new kind of uncertain cooperative game model is proposed with grey system and grey number operating regulations. A new grey Sharpley model is proposed to allocate benefits to the participants in a alliance with grey payoffs. More specifically, the grey Sharpley model is designed and proved its effectiveness, symmetry and additivity with grey number operation regulars. Besides the Raiffa solution is addressed to allocate profit in a large alliance and a multi-objective programming model is used to get the whitening result of the grey Sharpley model. A case study on an aircraft supply chain is conducted to demonstrate the feasibility and effectiveness of the new model. This paper expends the domain of the classic Sharpley model and constitutes a fresh perspective on benefit allocation under grey payoff information.