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来获知参与人数的机制。假设参与者可以以成本$c$创建新身份向拍卖方报告。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，而常规的Sybil攻击文献则假设攻击者$c$为零或有限值，其他"诚实"参与者$c$为无穷大。假名证明文献多假设成本为0。我们构建了包含可变成本的统一模型，将上述不同分支文献关联起来。通过将行动空间定义为"可创建身份集合"与"原始正规式博弈行动"的笛卡尔积，每个正规式博弈可扩展为Sybil博弈，其中每位参与者选择展示为多少个参与者以及其在原始博弈中的行动。若所有参与者自我报告不超过一个身份时满足（占优）激励相容，则该机制是（占优）假名证明的。我们研究了文献中针对匿名性与自我识别常态环境提出的若干机制，并给出了其不满足Sybil证明的条件。针对奖励共享问题，我们刻画了一类占优Sybil证明机制，并证明其达到效率上界。进一步，我们探讨了参与者可对其Sybil策略做出可信承诺时的扩展情形，并展示这种承诺如何破坏原本满足假名证明性质的机制。