Properties of contests: Constructing contest success functions from best-responses

Abstract

We aim at characterizing the functions that could be explained (recoverable) as a best reply of payoff-maximizing players in contests for a fixed prize. We show that recoverability strongly differs between Decisive Contests, where the prize is allocated with certainty, and Possibly Indecisive Contests, where the prize might not be awarded. In the latter, any arbitrary set of best reply functions is recoverable, thus "anything goes." In the former, best reply functions have to satisfy strong conditions in some cases. We provide an outline of possible applications of our results to R & D and labor markets.