This paper uses a two-country model with integrated markets for high-skilled labor to analyze the opportunities and incentives for national governments to provide higher education. Countries can differ in productivity, and education is financed through a wage tax, so that brain drain affects the tax base and has agglomeration effects. We study unilateral possibilities for triggering or avoiding brain drain and compare education policies and migration patterns in non-cooperative political equilibria with the consequences of bilateral cooperation between countries. We thereby demonstrate that bilateral coordination tends to increase public education expenditure compared to non-cooperation. At the same time, it aims at preventing migration. This is not necessarily desirable from the point of view of a social planner who takes account of the interests of migrants.