Agency costs in a supply chain with demand uncertainty and price competition

In this paper, we model a manufacturer that contracts with two retailers, who then choose retail prices and stocking quantities endogenously in a Bayesian Nash equilibrium. If the manufacturer designs a contract that is accepted by both retailers, it sets the wholesale price as a compromise between two conflicting roles: reducing intrabrand retail price competition and inducing retailers to stock closer to first-best levels (that is, optimum for the supply chain as a whole). In equilibrium, fill rates are less than first best. If, on the other hand, the manufacturer eliminates retail competition by designing a contract accepted by only one retailer, the assignment of consumers to retailers is inefficient. In either equilibrium, the performance of the supply chain is strictly less than first best. However, the manufacturer achieves first-best retail prices and fill rates if it can subsidize the retailers' leftover inventory. Absent such subsidies, the two-retailer equilibrium arises when the two retailers compete less intensively. In that equilibrium, numerical results indicate that the value of subsidizing unsold inventory is increasing in demand uncertainty, intensity of retail competition, and salvage value of inventory, and is decreasing in manufacturing cost and opportunity cost of shelf space.