Technical Note—Sequential Multiproduct Price Competition in Supply Chain Networks

We analyze a general model in which, at each echelon of the supply process, an arbitrary number of firms compete, offering one or multiple products to some or all of the firms at the next echelon, with firms at the most downstream echelon selling to the end consumer. At each echelon, the offered products are differentiated and the firms belonging to this echelon engage in price competition. The model assumes a general set of piecewise linear consumer demand functions for all products (potentially) brought to the consumer market, where each product’s demand volume may depend on the retail prices charged for all products; consumers’ preferences over the various product/retailer combinations are general and asymmetric . Similarly, the cost rates incurred by the firms at the most upstream echelon are general as well. We fully characterize the equilibrium behavior under linear price-only contracts, and we show how all equilibrium performance measures can be computed via a simple recursive scheme. Moreover, we establish how changes in the model parameters, in particular, exogenous cost rates or intercept values in the demand functions, impact the system-wide equilibrium. These comparative statics results allow for the quantification of cost pass-through effects and the measurement and characterization of the firms’ brand value. Lastly, we illustrate what qualitative impacts various changes in the structure of the supply chain network may bring forth.