Coordination in a supply chain with two manufacturers, two substitute products, and one retailer

This paper analyses a model of coordination in a supply chain consisting of two manufacturers, two products, and a single retailer under full information. Market demand for each of the manufacturer's products allows for both price and cross-price elasticities. We consider a Stackelberg game between the retailer and the two manufacturers and solve for the subgame perfect equilibrium wholesale price chosen by each of the manufacturers, the retail price charged by the retailer for each of two products, as well as the equilibrium demands for the two products. Unlike a classical dyadic supply chain, we show that only under certain allocations of the total profit between the manufacturers and the retailer is it the case that the vertically integrated chain is the preferred supply chain structure, even though it provides the highest total profit. An important result is that vertical integration is less advantageous when products are closer substitutes. We also show that a revenue sharing contract can coordinate this chain, but only when the manufacturers set their wholesale prices below their marginal costs of production. Finally, we show that the retailer can choose to integrate partially with one manufacturer to achieve a Pareto improving profit outcome.