Differential pricing for information sharing under competition

We consider a two-echelon supply chain with a manufacturer supplying to multiple downstream retailers engaged in differentiated Cournot competition. Each retailer has private information about uncertain demand. The manufacturer is the Stackelberg leader who sets the contract terms with the retailers, and benefits from retailers sharing their private information. When all retailers are given the same wholesale price, truthful information sharing is not an equilibrium outcome. We propose two variants of differential pricing mechanisms that induce truthful information sharing by all retailers. The first variant rewards a retailer for providing optimistic information and achieves truthful information sharing as a unique equilibrium. The differential pricing mechanism is optimal in the class of linear-price, incentive-compatible, direct mechanisms. The second variant, which incorporates provision for a fixed payment in addition to wholesale prices, preserves all the equilibrium properties of the first variant and additionally "nearly coordinates" the supply chain. Our analysis of differential pricing with a fixed payment provides interesting observations regarding the relationship between product substitutability, number of retailers, information precision, and market power. As products become closer substitutes and/or number of retailers increase, the manufacturer's market power increases, enabling her to extract a larger fraction of the supply chain surplus.