Recommendation Systems like YouTube are vibrant ecosystems with two types of users: Content consumers (those who watch videos) and content providers (those who create videos). While the computational task of recommending relevant content is largely solved, designing a system that guarantees high social welfare for \textit{all} stakeholders is still in its infancy. In this work, we investigate the dynamics of content creation using a game-theoretic lens. Employing a stylized model that was recently suggested by other works, we show that the dynamics will always converge to a pure Nash Equilibrium (PNE), but the convergence rate can be exponential. We complement the analysis by proposing an efficient PNE computation algorithm via a combinatorial optimization problem that is of independent interest.