We consider how group size affects the private provision of a public good with non-refundable binary contributions. A fixed amount of the good is provided if and only if the number of contributors reaches an exogenous threshold. The threshold, the group size, and the identical, non-refundable cost of contributing to the public good are common knowledge. Our focus is on the case in which the threshold is larger than one, so that teamwork is required to produce the public good. We show that both expected payoffs and the probability that the public good is obtained in the best symmetric equilibrium are decreasing in group size. We also characterize the limit outcome when group size converges to infinity and provide precise conditions under which the expected number of contributors is decreasing or increasing in group size for sufficiently large groups.

中文翻译：

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二元贡献博弈中的群体规模和集体行动

我们考虑团体规模如何影响私人提供不可退还的二元捐款的公共物品。当且仅当贡献者的数量达到外生阈值​​时，才提供固定数量的商品。门槛、团体规模以及为公益做出贡献的相同且不可退还的成本是众所周知的。我们关注的是阈值大于1的情况，因此需要团队合作才能产生公共物品。我们表明，预期收益和在最佳对称均衡中获得公共物品的概率随着群体规模的增加而减少。