In the realm of cost-sharing mechanisms, the vulnerability to Sybil strategies, where agents can create fake identities to manipulate outcomes, has not yet been studied. In this paper, we delve into the intricacies of different cost-sharing mechanisms proposed in the literature highlighting its non Sybil-resistance nature. Furthermore, we prove that under mild conditions, a Sybil-proof cost-sharing mechanism for public excludable goods is at least $(n/2+1)-$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 maintains its worst-case welfare under Sybil-strategies for every set of prior beliefs even when the mechanism is not Sybil-proof. Finally, we prove that the Shapley value mechanism for public excludable goods holds this property, and so deduce that the worst-case social cost of this mechanism is the $n$th harmonic number $\mathcal H_n$ even under equilibrium of the game with Sybil strategies, matching the worst-case social cost bound for cost-sharing mechanisms. This finding carries important implications for decentralized autonomous organizations (DAOs), indicating that they are capable of funding public excludable goods efficiently, even when the total number of agents is unknown.

翻译：在成本分摊机制领域，代理可通过创建虚假身份操纵结果的Sybil策略的脆弱性尚未得到研究。本文深入剖析文献中提出的不同成本分摊机制的复杂性，凸显其非抗Sybil特性。进一步地，我们证明在温和条件下，针对公共可排除物品的抗Sybil成本分摊机制至少具有$(n/2+1)-$近似比。这一发现揭示了在限制代理使用Sybil策略的环境中，最坏情况社会成本呈指数级增长。为规避这些负面结论，我们引入\textit{Sybil福利不变}机制的概念——即使机制本身不具备抗Sybil性，该机制仍能在任意先验信念集合下保持Sybil策略下的最坏情况福利。最后，我们证明公共可排除物品的Shapley值机制满足该性质，并由此推导出该机制的最坏情况社会成本为第$n$个调和数$\mathcal H_n$，即使在包含Sybil策略的博弈均衡中亦如此，这与成本分摊机制的最坏情况社会成本界相匹配。这一发现对去中心化自治组织具有重要启示，表明即便代理总数未知，该组织仍能高效地为公共可排除物品提供资金。