Alliance formation among perfectly complementary suppliers in a price-sensitive assembly system

Independent parties that produce perfectly complementary components may form alliances (or coalitions or groups) to better coordinate their pricing decisions when they sell their products to downstream buyers. This paper studies how market demand conditions (i.e., the form of the demand function, demand uncertainty, and price-sensitive demand) drive coalition formation among complementary suppliers. In a deterministic demand model, we show that for an exponential or isoelastic demand function, suppliers always prefer selling in groups; for a linear-power demand function, suppliers may all choose to sell independently in equilibrium. These results are interpreted through the pass-through rate associated with the demand function. In an uncertain demand model, we show that, in general, the introduction of a multiplicative stochastic element in demand has an insignificant impact on stable coalitions and that an endogenous retail price (i.e., demand is price sensitive) increases suppliers' incentives to form alliances relative to the case with a fixed retail price. We also consider the impact of various other factors on stable outcomes in equilibrium, e.g., sequential decision making by coalitions of different sizes, the cost effect due to alliance formation (either cost savings or additional costs), and a system without an assembler.