Cardinal contests

Abstract

We model and analyze cardinal contests, where a principal running a rank-order tournament has access to an absolute measure of the quality of agents' submissions in addition to their relative rankings. We show that a mechanism that compares each agent's output quality against a threshold to decide whether to award her the prize corresponding to her rank is optimal amongst the set of all mixed cardinal-ordinal mechanisms where the jth-ranked submission receives a fraction of the jth prize that is a non-decreasing function of the submission's quality. Furthermore, the optimal threshold mechanism uses exactly the same threshold for each rank.