Capacity Games in Assembly Systems with Uncertain Demand

An assembler needs sets of components, each produced by a different supplier. To produce the components and assemble the final product, the firms involved need to construct their individual production capacities before observing the actual demand. The firms have an incentive scheme (contract) to induce a "proper" capacity build-up. The key parameters of the contract are the set of transfer prices the assembler pays each supplier for a unit of its component. We consider two game settings as to how the terms of the contract are determined. The first is one where the assembler sets the prices, and the second is for the suppliers to simultaneously select the prices each wants to charge for its component. We first characterize the optimal capacity decision when the system is centralized, and then derive the decentralized equilibrium capacities under each of the two game settings. We show that the decentralized channel performances depend heavily on system structure/parameters. In particular, under the first setting, the performance improves as the assembler's share of the systemwide capacity cost increases and it is not affected by the number of suppliers in the system, while under the second setting, the performance degrades both in the assembler's share of capacity cost and in the number of suppliers. We show that the first setting dominates the second in terms of system performance if and only if the assembler's share of capacity cost is larger than the reciprocal of the number of firms involved.