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

This article focuses on designing a novel, flexible revenue-sharing contract between digital content platforms and app developers that accounts for heterogeneous beliefs about future revenues. Unlike current fixed-percentage or tiered commission contracts, the proposed contract features a continuous commission function based on current-period revenue and is derived using game theory and calculus of variations under the Nash bargaining framework. The study demonstrates that heterogeneous beliefs lead to nonlinear, piecewise linear contracts that can significantly improve expected profits—by over 100% in some cases—compared to the best linear contract, while maintaining or reducing negotiation complexity. Extensive numerical analyses, including scenarios with normally and Erlang-distributed revenues, show that the flexible contract outperforms linear benchmarks in 99% of cases, particularly when the platform is more optimistic about future revenue than the developer. The findings also provide insights into real-world practices, such as Apple's and Steam's differing commission policies, and suggest that flexible contracts can better address challenges arising from revenue uncertainty and limited transaction transparency in the digital products supply chain.