We introduce a game-theoretic framework that examines strategic interactions between a platform and its content creators in the presence of AI-generated content. Our model's main novelty is in capturing creators' dual strategic decisions: their investment in content quality and their (possible) consent to share their content with the platform's GenAI, both of which significantly impact their utility. To incentivize creators, the platform strategically allocates a portion of its GenAI-driven revenue to creators who share their content. We focus on the class of full-sharing equilibrium profiles, in which all creators willingly share their content with the platform's GenAI system. Such equilibria are highly desirable both theoretically and practically. Our main technical contribution is formulating and efficiently solving a novel optimization problem that approximates the platform's optimal revenue subject to inducing a full-sharing equilibrium. A key aspect of our approach is identifying conditions under which full-sharing equilibria exist and a surprising connection to the Prisoner's Dilemma. Finally, our simulations demonstrate how revenue-allocation mechanisms affect creator utility and the platform's revenue.