Sorting Contests and Contestants

We study the sorting of contestants across Tullock contests, and the allocation of a prize budget across these contests. Our benchmark result is that total effort is maximized by a unique grand contest and contestant exclusions decrease total effort. We consider two extensions of our benchmark result. First, we investigate expected winners' efforts maximization and find that the optimal sorting becomes one with pairwise high-type-only contests. Second, we investigate how to enlarge the strategy space of the designer so as to obtain a greater total effort than that of a unique grand contest, and we find that; (i) if the designer can make contestants' efforts valid for competing simultaneously in more than one contest, then total effort increases when sorting all contestants into a grand contest and low types only into a parallel contest with a smaller prize, and (ii) if the designer can tilt the playing field in favor of some contestants, then total effort increases even further when handicapping high types and sorting all contestants into a unique grand contest