Coordinating a Supply Chain System with Retailers Under Both Price and Inventory Competition

We investigate a supply chain system with a common supplier selling to downstream retailers who are engagedin both price andinventory competition. We establish the existence anduniqueness of the purestrategy Nash equilibrium for the retailer game and study how a supplier can coordinate the system to achieve the best performance. Our main conclusions are as follows: First, a buyback contract can be usedto coord inate retailers competing on both price andinventory in a sense that optimal retail prices andinventory levels arise as the Pareto-dominant equilibrium. With symmetric retailers, the system optimum arises as the unique symmetric equilibrium. Second, the particular type of competition experienced by retailers (price versus inventory competition) affects the characteristics of the contract. Specifically, strong price competition leads to a coordination mechanism with a positive buyback rate, where the supplier subsidizes retailers for leftover inventories; however, strong inventory competition leads to a negative buyback rate, where retailers are punished for overstocking. Using a linear expectedd emandfunction, we further explore the impact of system parameters on the coord ination contract andthe competitive equilibrium. We also findthat the performance of the supplier’s optimal contract is asymptotic to the system optimal coordination contract as competition becomes fierce.