OPTIMAL CONTEST DESIGN WITH NONLINEAR COSTS

Abstract

This paper studies the optimal contest design that maximises the total expected effort of potential players when they have nonlinear cost functions. The contest organiser aims to induce higher effort by utilising a combination of four instruments: shortlisting of potential players, entry sequence of participants (either simultaneous or sequential), entry fees paid by participants, and disclosure policy of the number of participants, whenever each is applicable. Shortlisted players decide whether to enter a contest upon observing the policy combination of the organiser. We derive and compare the optimal entry fees and optimal disclosure policy under each entry pattern for each number of shortlisted players. We find that the concavity (convexity) of the cost function plays a crucial role for the optimal design. Assuming that the contest is optimally designed after each entry pattern, simultaneous entry with a policy of disclosing the number of participants would induce the highest effort when costs are concave. While the optimal number of shortlisted players is not explicitly solved, at the optimum each of them enters stochastically. Alternatively, when costs are convex, the organiser would optimally include all potential players who at the optimum, would enter with certainty. All combinations of entry pattern and disclosure policy induce the same amount of effort at the optimum.