谁为连接性公共品买单？

中文摘要 AI 辅助

连接性可以将分散的贡献转化为一种公共品，使参与者和非参与者都受益。然而，只有参与者为其付费，并且每个参与者都可以通过退出而逃避其费用，同时仍能享受任何存续的公共产出。网络连接如何限制谁能够或必须付费，以及群体能够承受多大的成本？我们研究了一个参与博弈，其中公共产出等于活跃玩家最大连接群体的大小，该群体的成员分摊固定的运营成本。参与者因退出而破坏的产出是她的退出责任，并界定了她的支付上限。这些界限决定了群体的成本承受能力，并且，只要群体能够保持活跃，也决定了哪些参与者必须付费。我们证明，在至少包含五个玩家的连接网络中，路径网络唯一地最大化群体的成本承受能力，然而在均匀随机选择一名参与者退出后，它却最小化预期的存续产出。随着群体规模增长，最大承受能力与完全参与下社会总收益之比收敛于四分之一。因此，脆弱性可以增强自愿融资，但即使是融资能力最强的网络也无法弥合其创造的价值与参与者为维持其存续而愿意支付的费用之间的差距。

英文摘要

Connectivity can turn separate contributions into a public good that benefits participants and nonparticipants alike. Yet only participants pay for it, and each can avoid her charge by withdrawing while enjoying whatever public output survives. How do network connections constrain who can or must pay, and how large a cost can the group bear? We study a participation game in which public output equals the size of the largest connected group of active players, whose members divide a fixed operating cost. The output a participant destroys by withdrawing is her withdrawal responsibility and bounds her payment. These bounds determine the group's cost-bearing capacity and, whenever the group can be kept active, which participants must pay. We prove that among connected networks with at least five players, the path uniquely maximizes the cost-bearing capacity of a group, yet minimizes the expected surviving output after a uniformly selected participant withdraws. As the group grows, the ratio of maximal capacity to gross social benefit under full participation converges to one quarter. Fragility can therefore strengthen voluntary finance, but even the most financeable network cannot close the gap between the value it creates and what its participants will pay to sustain it.

发表机构

• Institute of Mathematics, Universidad Nacional Autónoma de México（墨西哥国立自治大学数学研究所）

机构由 AI 辅助整理，请以论文原文为准。