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 actual exponential increase in the worst-case social cost in environments where agents are restricted from using Sybil strategies. 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 with full support 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 in the DAO is unknown.

翻译：摘要：在成本分摊机制领域，针对代理可通过创建虚假身份操纵结果的女巫策略的脆弱性尚未被充分研究。本文深入剖析了文献中提出的不同成本分摊机制的复杂性，揭示了其非抗女巫攻击特性。进一步地，我们证明在温和条件下，针对公共可排他物品的抗女巫成本分摊机制至少具有$(n/2+1)$-近似比。这一发现表明，在禁止代理使用女巫策略的环境中，最坏情况下的社会成本实际上呈指数级增长。我们引入了\textit{女巫福利不变}机制的概念——即使机制不具备抗女巫攻击性，对于每一组具有完全支撑的先验信念，该机制在女巫策略下仍能保持其最坏情况下的福利水平。最后，我们证明针对公共可排他物品的沙普利值机制具有这一性质，并由此推导出该机制的最坏情况社会成本为第$n$调和数$\mathcal H_n$，这一结论即使在包含女巫策略的博弈均衡下依然成立，与成本分摊机制的最坏情况社会成本界限相匹配。该发现对去中心化自治组织（DAO）具有重要启示，表明即使在DAO中代理总数未知的情况下，其仍能高效资助公共可排他物品。