Alex Dickson | University of Strathclyde

This article investigates contests when heterogeneous players compete to obtain a share of a prize. We prove the existence and uniqueness of the Nash equilibrium when players have more general preferences than have been assumed in the literature thus far.  Our results show that many of the standard conclusions obtained in the analysis of contests---such as aggregate effort increasing in the size of the prize and the dissipation ratio invariant to the size of the prize---may no longer hold when more general preferences are accounted for. We derive the key conditions on preferences, which involve the rate of change of the marginal rate of substitution between a player's share of the prize and their effort within the contest, under which these results that depart from the conventional wisdom hold. Our approach nests conventional contest analysis as well as allowing for a much broader class of utility functions that capture diminishing marginal utility of the contest allocation, and interactions between contest effort and the (marginal) valuation of the contest allocation.

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