Contest design with uncertain performance and costly participation

Abstract

This paper studies the problem of designing contests for settings where a principal seeks to optimize the quality of the best contribution obtained, and potential contestants only strategize about whether to participate in the contest, as participation incurs some cost. This type of contest can be mapped to various real-life settings (e.g., selection of background actors based on headshots, photography contest). The paper provides a comparative game-theoretic based solution to two variants of the above underlying model: parallel and sequential contest, enabling a characterization of the equilibrium strategies in each. Special emphasis is placed on the case where the contestants are a priori homogeneous which is often the case in contests where ranking is mostly influenced by some probabilistic factors (e.g., luck) or whenever contestants are evaluated subjectively by a referee whose taste cannot be a priori predicted. Here, several (somehow counter-intuitive) properties of the equilibrium are proved, in particular for the sequential contest, leading to a comprehensive characterization of the principal's preference between the two.