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 that a Sybil-proof cost-sharing mechanism for public excludable goods under mild conditions is at least $(n+1)/2-$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 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——即代理通过创建虚假身份操纵结果的假名策略——的脆弱性尚未得到研究。本文深入探讨了文献中提出的各种成本分摊机制的细节，揭示了其非抗西比尔性。此外，我们证明了在温和条件下，针对公共可排除物品的抗西比尔成本分摊机制至少是$(n+1)/2$近似。这一发现揭示了在禁止代理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。为规避这些负面结果，我们引入了\textit{西比尔福利不变}机制的概念：当代理选择弱占优策略且对其他代理的行动持有主观先验信念时，该机制在西比尔策略下不会降低其福利。最后，我们证明了针对对称与子模成本函数的沙普利值机制具有这一性质，从而推导出该机制在含西比尔策略的均衡下的最坏情况社会成本为第$n$调和数$\mathcal H_n$，与成本分摊机制的最坏情况社会成本界限一致。这一发现表明，即使参与总人数未知，任何由具有私人估值的代理组成的群体均可实现无许可且匿名的公共可排除物品融资，其效率可与许可制及非匿名领域相媲美。