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Schweinzer, Paul and Segev, Ella (November 2008): The optimal prize structure of symmetric Tullock contests. SFB/TR 15 Discussion Paper No. 250
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Abstract

We show that the optimal prize structure of symmetric n-player Tullock tournaments assigns the entire prize pool to the winner, provided that a symmetric pure strategy equilibrium exists. If such an equilibrium fails to exist under the winner-take-all structure, we construct the optimal prize structure which improves existence conditions by dampening efforts. If no such optimal equilibrium exists, no symmetric pure strategy equilibrium induces positive efforts.