Flexible Revenue-Sharing Contract in a Digital-Content Supply Chain Under Heterogeneous Beliefs of the Parties

We study the design of a novel, flexible revenue-sharing contract between a platform and an app developer (or other digital content provider) when the parties hold heterogeneous beliefs with regard to the future income. The current contracts adopted by platforms in reality invoke a policy of two or three commission levels based on historical revenue data. We design a contract in which the commission is a continuous function of the revenue generated by the app or other digital content within the current period. In contrast to the majority of prior studies in operations management, which analyze the homogeneous beliefs scenario, we introduce heterogeneous beliefs, which turn out to be a crucial consideration in designing the contract structure. We use game theory and calculus of variations to derive the conditions to be satisfied by the flexible contract. Two criteria are used to evaluate the performance of the proposed flexible contract: the benefit gained by each party and the complexity of the negotiation (measured by the number of contract terms). The best linear contract serves as a performance benchmark. We show that the flexible contract has the potential to enhance the relationship between platforms and digital content providers. In particular, using extensive numerical analysis (based on 99,225 instances in a full factorial design), we demonstrate that the proposed contract may yield an improvement in expected profits of more than 100% compared with the best linear contract, and we identify the conditions under which the flexible contract achieves a substantial improvement relative to the benchmark. Moreover, the flexible contract outperforms the best linear contract in 99% of cases—the former is either more profitable while entailing the same level of negotiation complexity, or it has the same profitability but a lower level of negotiation complexity. In the remaining 1% of studied cases, the flexible contract is preferable in terms of profitability, but the best linear contract involves less negotiation friction, such that neither contract dominates the other. Based on real data, we demonstrate the applicability and advantages of the flexible contract for a scenario within the video games industry.