The market of digital educational resources and, in particular, online courses for the higher education system is actively developing. A significant role in creating a high-quality competitive online course is played by the organizational and legal system of interaction between authors and the university. This research article aims at developing a game-theoretical model of interaction between the participants of online course creating process in order to identify optimal (mutually beneficial) options and conditions for partnership interaction between the authors of online courses and the university. To represent the interaction between the authors and the university in terms of game theory, there are analyzed the specific features of creating an online course. The authors are the first to construct a mathematical game model for a typical situation of commercializing an online course within the university-and-author interaction. This situation is interpreted as a dynamic finite paired non-antagonistic non-cooperative game with complete perfect information. The Nash equilibrium, perfect on subgames, is found by the method of backward induction; the profile of optimal strategies is determined. The analysis of the results can help to substantiate, form and improve the strategy of mutually beneficial cooperation between the authors of the online course and the university.