Probabilistic Audit in a Revenue Sharing Contract Under Asymmetric Demand Information

Abstract

A two-echelon supply chain comprising a supplier and a retailer, coordinated by a revenue-sharing contract has been studied. The supplier knows the realized demand only from a sales report submitted by the retailer at the end of each decision period. Possession of private information about the market demand allows the retailer to under-report sales. To protect revenue loss from this under-reporting, the supplier uses audit probabilistically to check the retailer’s dishonesty. Unlike designing a mechanism for the supplier to elicit private information from the retailer, which has been predominantly discussed in the literature, this study proposes a policy where the players can improve their expected profit compared to what they would have earned when the retailer had to reveal truthful information. Our study finds that the supplier benefits from the retailer’s dishonesty, provided dishonesty is limited with the help of a probabilistic audit process. Both players' expected profits are higher in our proposed policy than what they would earn under a truth-inducing policy. These findings suggest that future studies focus on achieving social welfare instead of concentrating only on truth-inducing mechanisms. A numerical analysis of the optimization problem is performed to find the optimal audit probability. Our results will help a manager in a supplying firm design a revenue-sharing contract when she cannot observe her retailer’s revenue without an audit.