Supply chain coordination under competition

We study contracts between suppliers with fixed capacities of substitutable products and a single retailer. Suppliers present the retailer with contracts, and the retailer decides how much capacity to buy from each supplier and the quantity to sell in the market. We are interested in the form of the contracts in equilibrium, their effect on supply chain profit, and how profits are split between the suppliers and the retailer. Under mild assumptions on the supply chain profit as a function of sales, we show that in equilibrium suppliers use non-linear (sophisticated) contracts. Additionally, we characterize the set of equilibrium contracts, and show that all equilibria result in a coordinated chain with a unique profit split. The profit of each supplier is equal to the marginal contribution of her capacity to supply chain profits. Sophisticated contracts may harm some suppliers relative to the equilibrium profits resulting from wholesale price contracts.