With most content distributed online and mediated by platforms, there is a pressing need to understand the ecosystem of content creation and consumption. A considerable body of recent work shed light on the one-sided market on creator-platform or user-platform interactions, showing key properties of static (Nash) equilibria and online learning. In this work, we examine the {\it two-sided} market including the platform and both users and creators. We design a potential function for the coupled interactions among users, platform and creators. We show that such coupling of creators' best-response dynamics with users' multilogit choices is equivalent to mirror descent on this potential function. Furthermore, a range of platform ranking strategies correspond to a family of potential functions, and the dynamics of two-sided interactions still correspond to mirror descent. We also provide new local convergence result for mirror descent in non-convex functions, which could be of independent interest. Our results provide a theoretical foundation for explaining the diverse outcomes observed in attention markets.