摘要：We consider multi-stage elimination contests, where agents e¤orts at di¤erentstages generate some output for the organizers. Depending on the output functionwe characterize the optimal prize structure of the tournament and show that it is al-most e¢cient. We have found that in some cases quite a strange structure turns outto be optimal, under which prizes for agents are smaller at the later stages than atthe earlier ones. Su¢cient conditions for optimality of such structures are provided forthe case of a separable output function. Next we consider the modi cation, when thedesigner can specify a winning function. We provide su¢cient conditions for optimalityof a winning function and show that it can be found in the class of Tullock functions.This function does not depend on the output function. There is always an e¢cientequilibrium, under which the designer is able to extract the whole surplus from theagents and the corresponding optimal prize structure is always non-decreasing.
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