We study contests where the designer's objective is an extension of the widely studied objective of maximizing the total output: The designer gets zero marginal utility from a player's output if the output of the player is very low or very high. We model this using two objective functions: binary threshold, where a player's contribution to the designer's utility is 1 if her output is above a certain threshold, and 0 otherwise; and linear threshold, where a player's contribution is linear if her output is between a lower and an upper threshold, and becomes constant below the lower and above the upper threshold. For both of these objectives, we study (1) rank-order allocation contests that use only the ranking of the players to assign prizes and (2) general contests that may use the numerical values of the players' outputs to assign prizes. We characterize the contests that maximize the designer's objective and indicate techniques to efficiently compute them. We also prove that for the linear threshold objective, a contest that distributes the prize equally among a fixed number of top-ranked players offers a factor-2 approximation to the optimal rank-order allocation contest.
翻译:我们研究的是设计者的目标是为了扩大广泛研究的使总输出最大化的目标的延伸:设计者如果玩家的输出非常低或非常高,则其输出从玩家的输出中获得零边际效用。我们用两种客观功能来模拟这个功能:二进制门槛,一个玩家对设计者效用的贡献是1,如果她的输出超过某一临界值,则该设计者的贡献是线性,如果一个玩家的贡献是线性,如果她的输出在下限和上限之间,并且一直处于下限和上限以下,则该设计者的贡献是线性的。对于这两个目标,我们研究:(1) 单级分配竞赛只使用玩家的排名来分配奖项,和(2) 普通竞赛,可能使用玩家产出的数字值来分配奖项。我们描述这些竞赛的特征是使设计者的目标最大化,并指明有效计算这些奖项的技术。我们还证明,对于线性门槛目标而言,在固定数目的级别最高的玩家之间平等分配奖项的竞赛提供了与最佳等级分配竞赛的系数-2近。