A bargaining framework in supply chains: The assembly problem

We examine a decentralized supply chain in which a single assembler buys complementary components from n suppliers and assembles the final product in anticipation of demand. Players take actions in the following sequence. First (stage 1), the suppliers form coalitions among themselves. Second (stage 2), the coalitions compete for a position in the negotiation sequence. Finally (stage 3), the coalitions negotiate with the assembler on allocations of the supply chain's profit. We model the multilateral negotiations between the suppliers and the assembler sequentially, i.e., the assembler negotiates with one coalition at a time. Each of these negotiations is modeled using the Nash bargaining concept. Further, in forming coalitions we assume that players are farsighted. We then predict at equilibrium the structure of the supply chain as a function of the players' relative negotiation powers. In particular, we show that the assembler always prefers the outcome where suppliers do not form coalitions. However, when the assembler is weak (low negotiation power) the suppliers join forces as a grand coalition, but when the assembler is powerful the suppliers stay independent, which is the preferred outcome to the assembler.