Endogenous Contest Success Functions: A Mechanism Design Approach

*Leonid Polishchuk
Higher School of Economics, Moscow

Alexander Tonis
New Economic School, Moscow

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     Last modified: November 23, 2010
     Presentation date: 03/12/2011 4:30 PM in NH 1120, Session A
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Abstract
We describe optimal contest success functions (CSF) which maximize expected revenues of an administrator who allocates under informational asymmetry a source of rent among competing bidders. It is shown that in the case of independent private values rent administrator's optimal mechanism can always be implemented via some CSFs as posited by Tullock. Such optimal endogenous CSFs are shown to have properties which are commonly assumed a priory as plausible features of rent-seeking contests. We identify conditions when optimal mechanisms entail logit CSFs, and similarly, in the case of variable resource, cooperative production-type CSFs. A simple unidimensional approximation of optimal CSFs is offered for large numbers of participating agents.

Analysis of endogenous CSFs reveals origins of ex post efficiency losses in rent-seeking, including the failure to achieve socially optimal investments into rent-generating resources. Such losses are in fact preventable, since there always exist ex post efficient incentive-compatible Groves mechanisms satisfying all feasibility constraints, but those mechanisms will not be selected by a revenue-maximizing resource administrator.