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，代理人通过创建虚假身份操纵结果的“女巫策略”尚未得到充分研究。本文深入探讨了文献中提出的多种成本分摊机制的复杂性，揭示了它们缺乏女巫抗性。进一步地，我们证明在温和条件下，针对公共排他品的抗女巫成本分摊机制至少达到 $(n/2+1)$-近似比。这一发现表明，在限制代理人使用女巫策略的环境中，最坏情况下的社会成本将呈指数级增长。为规避这些负面结果，我们引入 $\textit{女巫福利不变}$ 机制的概念——即使机制不具备抗女巫性，该机制仍能在任何先验信念集合下保持女巫策略下的最坏情况福利。最后，我们证明公共排他品的Shapley值机制具备该性质，从而得出：即便在存在女巫策略的博弈均衡下，该机制的最坏情况社会成本为第 $n$ 个调和数 $\mathcal H_n$，与成本分摊机制的最坏情况社会成本上界一致。这一发现对去中心化自治组织（DAOs）具有重要启示：即使代理人总数未知，它们仍能有效为公共排他品融资。