Platform sponsors strive to govern their platform ecosystem to be generative in supplying complementary products abreast of adoption targets. A more comprehensive pool of adopters requires high value creation capacity. Leveraging the opening of borders to complementors for competing in adoption could be a winning strategy when fostering generativity. Seldom has this view been studied empirically; therefore, the present study examines the effects of supply-side openness on platform adoption and investigates generativity's role between them as a mediator. Moreover, the study explores the heterogeneity between early and late adopters in generativity's influence. We also analyze generativity in mediating the effect of openness by the moderating influence of technological complexity. Consequently, a moderated mediation analysis is employed on panel data of 8960 video games in six platforms and three regions. Results show that platforms' openness propels their adoption, and generativity mediates this effect. Specifically, this study clarifies the idea that supply-side openness, the proliferation of more open innovation strategies, enhances platforms' value generation capacity, and both enhance platform adoption. Findings also indicate that platforms' technological complexity positively moderates the mediation role of generativity, revealing that in more complex platforms, openness increases generativity more intensely.