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，对 Sybil 策略（亦称假名策略，即参与者通过创建虚假身份操纵结果的策略）的脆弱性尚未得到系统研究。本文深入剖析已有文献中提出的各类成本分摊机制，揭示其缺乏抗 Sybil 特性的本质。进一步证明，在温和条件下，针对公共可排他物品的抗 Sybil 成本分摊机制至少达到 $(n+1)/2$ 近似比。这一发现表明，在限制参与者使用 Sybil 策略的环境中，最坏情形社会成本呈指数增长。为规避这些负面结论，我们提出 \textit{Sybil 福利不变}机制的概念——当参与者选择弱占优策略并对他者行为持有主观先验信念时，该机制在 Sybil 策略下不会降低社会福利。最终证明，针对对称且子模成本函数的 Shapley 值机制具备该性质，由此推导出该机制在 Sybil 策略均衡下的最坏情形社会成本为第 $n$ 个调和数 $\mathcal H_n$，与成本分摊机制的最坏情形社会成本界一致。该结论表明，即使参与总人数未知，任何由具有私有估值的参与者组成的群体，均可在无需许可且匿名的条件下资助公共可排他物品，并实现与许可认证及实名领域相当的社会效率。