This paper shows that donors that maximize relative aid impact spread their budgets across many recipient countries in a unique Nash equilibrium, explaining aid fragmentation. This equilibrium may be inefficient even without fixed costs, and the inefficiency increases in the equality of donors budgets. The paper presents empirical evidence consistent with theoretical results. These imply that, short of ending donors maximization of relative aid impact, agreements to better coordinate aid allocations are not implementable. Moreover, since policies to increase donor competition in terms of aid effectiveness risk reinforcing relativeness, they may well backfire, as any such reinforcement increases aid fragmentation.