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的机制，而必须依赖参与者的自我报告来了解参与人数。假设参与者可以花费成本 \(c\) 创建新身份向拍卖者报告。常规机制设计范式隐含地假设所有参与者的 \(c\) 为无穷大，而常规Sybil攻击文献则假设攻击者的 \(c\) 为零或有限值，其他"诚实"参与者的 \(c\) 为无穷大。假名证明文献多数假设成本为0。我们提出一个包含可变成本的统一模型，将上述分散的研究方向纳入统一框架。通过将行动空间定义为可创建身份集合（每个参与者可选择以多少身份参与博弈）与原始正规型博弈行动集合的乘积，可将范式性正规型博弈扩展为Sybil博弈。若机制对参与者自发报告至多一个身份具有（占优）激励兼容性，则该机制是（占优）假名证明的。我们研究了文献中以匿名和自识别为常态场景下提出的相关机制，给出其不满足Sybil证明性的条件。针对奖励共享场景，我们刻画了一类占优Sybil证明机制，并证明其可达效率上界。最后，我们考虑参与者可对其Sybil身份策略进行可信承诺的扩展情形，论证这种承诺如何能够破坏原本具有假名证明性的机制。