We investigate the temporal structure that maximizes the winner’s effort in large homogeneous contests. We find that the winner’s effort ranges from a lower bound of 0 to an upper bound of one third of the value of the prize, depending on the temporal structure; the upper (lower) bound is approached with an infinite number of players playing sequentially (simultaneously) in the first periods (period). Nevertheless, when the number of players is large but finite, we show that winner’s effort is maximized when all players play sequentially except in the very last period and that, within the family of such optimal temporal structures, more players play simultaneously in the very last period than sequentially in all other periods. Furthermore, out of all players, the percentage of those playing simultaneously in the very last period goes to 100% as the number of players grows larger and larger.

我们研究了最大化获胜者的时间结构在大型同质竞赛中努力。我们发现获胜者的努力范围从 0 的下限到奖品价值的三分之一的上限，具体取决于时间结构；在第一个时期（时期）中，无限数量的玩家依次（同时）进行游戏，从而达到上限（下限）。然而，当玩家数量很大但有限时，我们表明，当所有玩家按顺序进行游戏时，获胜者的努力会最大化，除了最后一个时期，并且在这种最佳时间结构的家族中，更多的玩家在最后一个时期同时玩期间比在所有其他期间按顺序排列。此外，在所有玩家中，随着玩家数量的增加，最后一期同时玩的比例达到100%。