Blavatskyy, Pavlo R (2004). Why the Olympics have three prizes and not just one. Working paper series / Institute for Empirical Research in Economics No. 200, University of Zurich.
There are at least two reasons why multiple prizes can be optimal in symmetric imperfectly discriminating contests. First, the introduction of multiple prizes reduces the standard deviation of contestants' effort in asymmetric equilibria, when the majority of contestants actively participate in competition. Second, the introduction of multiple prizes may increase the aggregate (average) effort contributed in the contest. When more of a total prize fund is shifted away from the first prize, on the one hand, the active contestants obtain an incentive to reduce their individual effort, but, on the other hand, the number of active contestants may increase. Therefore, the aggregate (average) effort may increase when the number of active contestants in equilibrium increases.
There are at least two reasons why multiple prizes can be optimal in symmetric imperfectly discriminating contests. First, the introduction of multiple prizes reduces the standard deviation of contestants' effort in asymmetric equilibria, when the majority of contestants actively participate in competition. Second, the introduction of multiple prizes may increase the aggregate (average) effort contributed in the contest. When more of a total prize fund is shifted away from the first prize, on the one hand, the active contestants obtain an incentive to reduce their individual effort, but, on the other hand, the number of active contestants may increase. Therefore, the aggregate (average) effort may increase when the number of active contestants in equilibrium increases.
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