Abstract
We examine the properties of all-pay contests in the spirit of Moldovanu and Sela (2001) as the number of entrants grows large under organizer objectives of expected and expected maximum outcomes. Unlike the case with a small number of entrants, with a large number of entrants a single prize becomes optimal even for an organizer with concave utility. Diminishing returns or risk-aversion on the part of the organizer do not justify multiple prizes in large contests. With optimal prizes determined asymptotically, we characterize the limiting value of outcomes in an optimal contest; exactly in the case of linear production and up to bounds in the concave/convex case. In all cases the limiting value is bounded away from zero. In the linear case, the limit is one-half the maximum feasible outcome.
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