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A noncooperative network is considered, in which each user routes its flow in a way that optimizes its individual performance objective. Nash equilibria characterize the operating points of the network. The network designer aims to allocate link capacities, so that the resulting Nash equilibria are efficient, according to some system-wide performance criterion. In a noncooperative setting, the solution of such design problems is, in general, complex and at times counterintuitive, since adding link capacity might lead to degradation of user performance. For systems of parallel links, it is shown that such paradoxes do not occur and that the capacity allocation problem has a simple and intuitive optimal solution, that coincides with the solution in the single-user case. Extensions to general network topologies are also derived.