Player strength and effort in contests

Abstract

n competitive settings, disparities in player strength are common. It is intuitively unclear whether a stronger player would opt for larger or smaller effort compared to weaker players. Larger effort could leverage their strength, while lower effort might be justified by their higher probability of winning regardless of effort. We analyze contests with three or more players, exploring when stronger players exert larger or lower effort. To rank efforts, it suffices to compare marginal utilities in situations where efforts are equal. Effort ranking depends on differences in hazard rates (which are smaller for stronger players) and reversed hazard rates (which are larger for stronger players). Compared to weaker players, stronger players choose larger effort in winner-takes-all contests and lower effort in loser-gets-nothing contests. Effort rankings can be non-monotonic in contests with several identical prizes, and they depend on the slopes of players' pdfs in contests with linear prize structure.