Coalition Analysis on Two Manufactures and Two Retailers Supply Chain via Cooperative Game Theory

In this study, we consider a coalition analysis on the pricing problem for a decentralized supply chain model in which two manufacturers and two retailers with price competitions. In the pricing game, we analyze the equilibrium solutions with perfect competition, grand coalition and partial cooperation between manufacturers and retailers. The results show the externality between coalitions for supply chain members. Therefore, the pricing game is represented as a partition function game. The stable profit allocation in each alliance structure is obtained based on cooperative game theory for the partition function game. We derive the new finding that if there are multiple partial alliances within the same alliance structure, the profit within the partial alliance is smaller than the profit when there is only one partial alliance. Then, it is shown that the pessimistic and optimistic Shapley values of the manufacturers are lower than the optimistic personal alliance value of the manufacturer when the product substitutability is lower and the store substitutability is higher.