Intertemporal Contracting in a Supply Chain

The paper studies a stylized supply chain, consisting of a manufacturer who sells a particular product to an independent retailer. The aim is to study intertemporal coordination and contracting in the supply chain, using a franchise contract. A franchise contract includes as special cases a wholesale‐price contract, a two‐part tariff, and a revenue‐sharing contract. The retailer determines her ordering rate and the consumer price while the manufacturer determines the production rate and the parameters of the franchise contract. Contract parameters are time‐dependent and determined under two, alternative, objectives. First, the manufacturer wishes to achieve an outcome in which total supply chain profits are maximized. Second, the manufacturer seeks an outcome which maximizes its individual profits. The setup is a differential game played over a fixed and finite horizon.