We model competing groups when players' values for winning are private information, the effort complementarity is uncertain at the time efforts are exerted, and the group with the best performance wins the contest. We analyze the effects of increasing the number of team members and the anticipated complementarity of efforts. We find that the effort underprovision brought about by a larger group membership is especially severe if the complementarity is high. More generally, higher complementarity may exacerbate rather than alleviate the underprovision of effort. Members of groups that are otherwise symmetric—and only differ with respect to the anticipated complementarity of efforts—use the same equilibrium strategy. And, when groups differ only in size, members of the smaller group act more aggressively, but the smaller or larger group may be more likely to win.

中文翻译：

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具有互补性的私人信息团体竞赛

当玩家的获胜价值是私人信息时，我们对竞争群体进行建模，在付出努力时努力的互补性是不确定的，表现最好的群体赢得比赛。我们分析了增加团队成员数量的影响以及预期的工作互补性。我们发现，如果互补性很高，则由更大的组成员所带来的努力不足尤其严重。更一般地说，更高的互补性可能会加剧而不是减轻努力的不足。其他对称的群体成员——只是在预期的努力互补性方面有所不同——使用相同的均衡策略。而且，当群体仅在规模上有所不同时，较小群体的成员会采取更积极的行动，