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Loss of coordination in a competitive supply chain with pre-orders and endogenous pricing

In this work, we investigate a two-tier supply chain in which there is a supplier offering price-only contracts to several retailers who face stochastic demand. Each retailer has to determine his price before taking pre -orders and his demand depends on the prices of all retailers in the market. We assume the expected demand function is affine. We analyze two scenarios when retailers compete with substitutes or complements. In contrast to most existing literature which typically assumes symmetric retailers with a homogeneous product, we study asymmetric price-setting retailers with differentiated products. We derive tight upper and lower bounds on the profit loss due to lack of coordination in the supply chain. Our results show that when retailers compete with substitutes, horizontal competition among retailers compensates the double marginalization effect and promotes efficiency. Furthermore, the loss of profit in the decentralized setting is no more than 25% of the optimal profit in the centralized setting. This implies that in a substitutable product market, there is limited room for improvement from more elaborate contracts, which are often costly to implement. The opposite happens for complements, where horizontal competition aggravates the double marginalization effect and further deteriorates the chain-wide efficiency. It suggests that large profit gains can be achieved through more complex contracts which coordinate the chain.