For two centuries, academics and their universities have competed for prominence and vied to demonstrate that their institutions are at the center of the scholarly world. Scientific advances in particular fields, reciprocal academic visits and conferences, impressive physical architecture, and publishing in shared venues and a "lingua franca" are among the many dimensions in which universities seek prestige in a relational status system. We call this system "competitive emulation" and theorize it as a mode of rivalry neither fully captured by imaginaries of economic and political competition nor eclipsed by third-party ranking schemes. By nuancing university competition this way, we emphasize its fragility, dynamism, and relationality, and suggest how this special form of competition might be leveraged for strategic action in our current times.