Optimal exclusivity strategy for digital service on competing platforms with different installed bases

Exclusive digital services are increasingly prevalent on growing digital service platforms. This study explores the optimal exclusivity strategy for digital service developers and examines the negotiation of licensing fees in exclusive agreements between developers and platforms. We develop a game-theoretic model in which a developer offers a digital service to consumers through competing platforms, one of which is superior in terms of installed base and bargaining power in negotiations with the developer. One interesting finding is that the inferior platform may pay a lower licensing fee to the developer than the superior platform when the difference in their installed bases is small. As the superior platform's installed base grows, its equilibrium licensing fee increases if its bargaining power is low but decreases if it is high. Furthermore, our analysis reveals that exclusivity on the superior platform is more profitable for the developer when the inferior platform's installed base is sufficiently small. Conversely, when the inferior platform's installed base is large, the developer prefers exclusivity on the inferior platform if the number of new consumers is sufficiently large, and non-exclusivity otherwise. Finally, we find that consumer surplus is always highest under the non-exclusivity strategy, while social welfare reaches its maximum under the non-exclusivity strategy only when the platform with lower intrinsic value has a sufficiently large installed base.