We give the conditions for the attainment of self-enforcing Pareto efficiency under complete effort non-observability, strict agent rationality and global budget balance among teams involved in a winner-takes-all contest for a prize. Employing Nash conjectures and fixed fee financing of the prize, we characterize the competitive environment that allows teams to overcome the moral hazard problem and induce self-enforcing egalitarian outcomes. If the number of identical teams is finite, the production technology is restricted to factor symmetric ones. When the number of identical teams becomes unbounded, the restriction on the production technology vanishes and there always exists a fee level that supports a self-enforcing Pareto efficient solution as long as member utilities over own share are identical and obey the Inada conditions. Some form of membership symmetry cannot be ruled out for Pareto efficiency.