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This contribution discusses some recent theoretical contributions dealing with competition in markets for higher education. In a market for students subject to network effects, we discuss the various forms of inefficiencies which might result from competition between universities. It is shown that the bulk of these inefficiencies might be reduced through some simple ex ante coordination devices controlled by the public authority. In a university where departments compete among themselves for the allocation of the university budget, it is shown how the organization of this competition by the central authority might be instrumental in enforcing incentive schemes which enhance teaching quality and research effort.