Consider a mechanism that cannot observe how many players there are directly, but instead must rely on their self-reports to know how many are participating. Suppose the players can create new identities to report to the auctioneer at some cost $c$. The usual mechanism design paradigm is equivalent to implicitly assuming that $c$ is infinity for all players, while the usual Sybil attacks literature is that it is zero or finite for one player (the attacker) and infinity for everyone else (the 'honest' players). The false-name proof literature largely assumes the cost to be 0. We consider a model with variable costs that unifies these disparate streams. A paradigmatic normal form game can be extended into a Sybil game by having the action space by the product of the feasible set of identities to create action where each player chooses how many players to present as in the game and their actions in the original normal form game. A mechanism is (dominant) false-name proof if it is (dominant) incentive-compatible for all the players to self-report as at most one identity. We study mechanisms proposed in the literature motivated by settings where anonymity and self-identification are the norms, and show conditions under which they are not Sybil-proof. We characterize a class of dominant Sybil-proof mechanisms for reward sharing and show that they achieve the efficiency upper bound. We consider the extension when agents can credibly commit to the strategy of their sybils and show how this can break mechanisms that would otherwise be false-name proof.

翻译：考虑一个无法直接观测参与者数量，而必须依赖其自我报告以知悉参与人数的机制。假设参与者可以以成本$c$创建新身份向拍卖者报告。传统机制设计范式等价于隐式假设所有参与者的$c$为无穷大，而传统Sybil攻击文献则假设该成本对一名参与者（攻击者）为零或有限，对其他所有“诚实”参与者为无穷大。假名证明文献大多假设成本为零。我们提出一个包含可变成本的统一模型，将上述不同分支纳入同一框架。通过将行动空间定义为可创建身份集合与原规范式博弈行动集合的笛卡尔积——其中每位参与者决定以多少身份参与博弈以及在原规范式博弈中的行动——可将一个典型的规范式博弈扩展为Sybil博弈。若某机制对所有参与者而言，以最多一个身份进行自我报告是（占优）激励相容的，则该机制为（占优）假名证明机制。我们研究文献中针对匿名性与自我识别为常态场景提出的机制，并给出其不满足Sybil证明特性的条件。针对收益共享问题，我们刻画了一类占优Sybil证明机制，并证明其可实现效率上界。我们还探讨了参与者可对其Sybil身份策略做出可信承诺的扩展情形，并展示此类承诺如何破坏本应具备假名证明特性的机制。