Decentralized pricing and capacity decisions in a multitier system with modular assembly

We model a modular assembly system in which a final assembler outsources some of the assembly task to first-tier suppliers (subassemblers), who produce modules made up of multiple components. The assembler sets module prices it will pay to the subassemblers, the subassemblers set component prices they will pay to suppliers, and then all players choose how much capacity to install, with the minimum capacity choice determining system capacity. Finally, stochastic end-product demand is observed and all players produce (and are paid for) the same number of units-the minimum of demand and system capacity. We characterize equilibrium price and capacity choices, and then use that characterization to derive results regarding higher-level structural choices by the assembler-such as how to group components into modules and which suppliers to choose as subassemblers. We also compare performance of the system to a traditional assembly system with an assembler and suppliers but without subassemblers.