Alliance formation in assembly systems with quality-improvement incentives

We study an assembly system where n upstream complementary suppliers produce components and sell them to a downstream manufacturer. The manufacturer assembles all the components into final products and sells them in the final market. The demand for final products is assumed to be deterministic and sensitive to both the selling price set by the manufacturer and the quality-improvement effort levels of all suppliers. The suppliers may form coalitions to better coordinate their wholesale pricing and quality-improvement effort decisions. We analyze the stability of coalition structures by adopting farsighted stability concepts. To characterize supplier’s profit allocation in a coalition, we consider three allocation rules, including the equal allocations, the proportional allocations and the Shapley value allocations. The results show that the grand coalition is always stable under both the equal allocations and the proportional allocations. However, under the Shapley value allocations, the grand coalition is stable only when the suppliers’ quality efficiencies have relatively small differences. Conditions under which the suppliers will not act independently are presented as well. Because of the positive externalities of quality improvements, we demonstrate that coalitions of suppliers with lower quality efficiencies could benefit from free-riding on the investments of coalitions of suppliers with higher quality efficiencies in the system.