Supply Chain Competition with Multiple Manufacturers and Retailers

We study competition in a supply chain where multiple manufacturers compete in quantities to supply a set of products to multiple risk-averse retailers who compete in quantities to satisfy the uncertain consumer demand. For the symmetric supply chain, we give closed-form expressions for the unique equilibrium. We find that, provided there is a sufficiently large number of manufacturers and retailers, the supply chain efficiency (the ratio of the aggregate utility in the decentralized and centralized chains) can be raised to one by inducing the right degree of retailer differentiation. Also, risk aversion results in triple marginalization: retailers require a strictly positive margin to distribute even when they are perfectly competitive, as otherwise they are unwilling to undertake the risk associated with the uncertainty in demand. For the asymmetric supply chain, we show how numerical optimization can be used to compute the equilibria, and find that the supply chain efficiency may drop sharply with the asymmetry of either manufacturers or retailers. We also find that the introduction of asymmetric product assortment reduces the degree of competition among retailers, and thus has an effect similar to that of reducing the number of retailers. We show that, unlike in the symmetric chain, the asymmetric chain efficiency depends on product differentiation and risk aversion, because of the interaction between these features and the asymmetry of manufacturers and retailers.