We develop a model of two parallel contests, asymmetric in quantity of homogeneous prizes open to contest, with a finite number of homogeneous risk-neutral bidders. Whether the bidder upon entry into a particular contest is aware of the realized number of competing contestants in the contest is irrelevant to the expected effort at equilibrium. At equilibrium the expected effort per capita in the larger contest (the contest with more prizes) is greater than that in the smaller one. The larger contest nonetheless does not attract enough contestants to achieve optimum in rent extraction from the bidders.

中文翻译：

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平行竞赛模型

我们开发了两个平行竞赛的模型，开放竞赛的同质奖品数量不对称，同质风险中性投标者数量有限。投标人在参加特定比赛时是否知道比赛中竞争者的实际数量与预期的平衡努力无关。在均衡情况下，大型竞赛（奖品较多的竞赛）中的人均预期努力大于小型竞赛中的人均努力。尽管如此，规模更大的比赛并没有吸引足够的参赛者来从投标人那里获得最佳租金。