In the realm of cost-sharing mechanisms, the vulnerability to Sybil strategies -- also known as false-name strategies, where agents create fake identities to manipulate outcomes -- has not yet been studied. In this paper, we delve into the details of different cost-sharing mechanisms proposed in the literature, highlighting their non-Sybil-resistant nature. Furthermore, we prove no deterministic, anonymous, truthful, Sybil-proof, upper semicontinuous, and individually rational cost-sharing mechanism for public excludable goods is better than $\Omega(n)$-approximate. This finding reveals an exponential increase in the worst-case social cost in environments where agents are restricted from using Sybil strategies. To circumvent these negative results, we introduce the concept of \textit{Sybil Welfare Invariant} mechanisms, where a mechanism does not decrease its welfare under Sybil strategies when agents choose weak dominant strategies and have subjective prior beliefs over other players' actions. Finally, we prove that the Shapley value mechanism for symmetric and submodular cost functions holds this property, and so deduce that the worst-case social cost of this mechanism is the $n$th harmonic number $\mathcal H_n$ under equilibrium with Sybil strategies, matching the worst-case social cost bound for cost-sharing mechanisms. This finding suggests that any group of agents, each with private valuations, can fund public excludable goods both permissionless and anonymously, achieving efficiency comparable to that of non-anonymous domains, even when the total number of participants is unknown.ess and anonymously, achieving efficiency comparable to that of permissioned and non-anonymous domains, even when the total number of participants is unknown.

翻译：在成本分摊机制领域，针对西比尔策略（亦称虚假身份策略，即参与者通过伪造身份操纵结果的策略）的脆弱性尚未得到系统研究。本文深入剖析了文献中提出的多种成本分摊机制的细节特征，揭示其缺乏抗西比尔攻击能力的本质。进一步地，我们证明对于公共可排除物品而言，不存在具有确定性、匿名性、真实性、抗西比尔性、上半连续性和个体理性特性的成本分摊机制能够达到优于$\Omega(n)$近似比。这一发现表明，在限制参与者使用西比尔策略的环境中，最坏情况下的社会成本呈指数级增长。为规避上述负面结论，我们提出"西比尔福利不变"机制概念——当参与者选择弱优势策略且对其他玩家行动持有主观先验信念时，该类机制在面临西比尔策略时不会降低社会福利。最后，我们证明针对对称子模成本函数的沙普利值机制具备该特性，并由此推导出该机制在面临西比尔策略的均衡状态下，最坏情况社会成本为第$n$个调和数$\mathcal H_n$，这与成本分摊机制的社会成本最坏情况上界一致。该发现表明，即使总参与者数量未知，任何具有私有估值的参与者群体都能以无需许可且匿名的方式为公共可排除物品融资，实现与许可型非匿名领域相当的社会效率。