Dynamic Pricing in Online Education: A Stochastic Differential Game of Reference Price and Instructor Effects

This paper reveals a fundamental conflict at the heart of the online education partnership between platforms and their instructors. While intuition suggests that flexible dynamic pricing benefits all parties, our analysis uncovers a critical and counterintuitive trade-off: the platform’s profit-maximizing pricing strategy can systematically reduce the instructor’s earnings. We model this strategic interaction using a game-theoretic framework that incorporates both instructor-driven course quality and learners’ evolving psychological reference prices (their expectations of a fair price). By analyzing three scenarios (basic, static, and fully dynamic), we demonstrate how this conflict between platform optimization and instructor incentives arises. This central finding highlights a significant managerial challenge: platforms must balance short-term revenue gains from dynamic pricing against the long-term need to retain high-quality instructors. An extension of the model to include market uncertainty (stochastic effects) further demonstrates the robustness of this core finding. The results suggest that while platforms can leverage dynamic pricing even in volatile markets, they must simultaneously implement safeguards, such as fair revenue-sharing agreements, to protect instructor incentives and ensure a sustainable partnership.