A cooperative game theory approach for the equal profit and risk allocation

This paper focuses on the decentralized systems that use the revenue-sharing and cost-sharing contracts as coordination mechanisms. We consider a grand-coalition N with finite players, who agree to cooperate by undertaking part of the system's cost individually, while the remaining costs C and revenues R are shared properly, in order to allocate the system's profits and risks equally among them. We use cooperative game theory, in order to examine the possible coalitions of players and to estimate the finite set of solutions, with which the system's profits and risks are allocated equally among all players. Specifically, each system's solution consists of a pair of vectors r, c ∈ RN, with which all player profits are normally distributed with equal mean values and variances. Moreover, we introduce a code that can be used for the computation of the precise number of possible solutions.