Player strength and effort in contests
研究了多奖项竞赛中实力不同的选手如何选择努力水平，发现实力强的选手在赢家通吃时更努力，在输家全无时更不努力，且努力排名在多个相同奖项时可能非单调。
In 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 multi-prize contests with three or more heterogeneous 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.