Academic institutions seek to enhance their reputation, which is one of their primary assets. Doing so requires a massive investment of resources in research, recruiting a high-quality academic staff, and building campuses and state-of-the-art laboratories. To obtain the necessary financial resources, institutions must attract students, donors, and government budgets and grants. This paper introduces a stylized dynamic model demonstrating how an institution can best allocate its resources between teaching and research. We create a simulated competition that resembles the real situation in which the burnishing of the institution’s reputation depends not only on its resource allocation but also on its competitors’ actions and reputation. We consider a two-institution contest over time using a differential game solution with open-loop strategies. In this case, a steady-state solution has a weaker effect on research but a stronger effect on teaching.