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Optimal elimination contest

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  • Knyazev, Dmitriy

Abstract

We consider multi-stage elimination contests, where agents’ efforts at different stages generate some output for the organizers. Depending on the output function we characterize the optimal prize structure of the tournament and show that it is almost efficient. We have found that in some cases quite a strange structure turns out to be optimal, under which prizes for agents are smaller at the later stages than at the earlier ones. Sufficient conditions for optimality of such structures are provided for the case of a separable output function. Next we consider the modification, when the designer can specify a winning function. We provide sufficient conditions for optimality of 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 efficient equilibrium, under which the designer is able to extract the whole surplus from the agents and the corresponding optimal prize structure is always non-decreasing.

Suggested Citation

  • Knyazev, Dmitriy, 2013. "Optimal elimination contest," Bonn Econ Discussion Papers 09/2013, University of Bonn, Bonn Graduate School of Economics (BGSE).
  • Handle: RePEc:zbw:bonedp:092013
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    References listed on IDEAS

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    More about this item

    Keywords

    Tullock contests; multiple-stage tournament; optimal structure; negative prizes;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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