We show that in the single-parameter mechanism design environment, the only non-wasteful, symmetric, incentive compatible and Sybil-proof direct mechanism is a second price auction with symmetric tie-breaking. Thus, if there is private information, lotteries or other mechanisms that do not always allocate to a highest-value bidder are not Sybil-proof or not incentive compatible. Moreover, we show that our main (im)possibility result extends beyond linear valuations, but not to multi-unit object allocation with capacity constrained bidders. We also provide examples of mechanisms (with higher interim payoff for the bidders than a second price auction) that satisfy all of the other axioms and a weaker, Bayesian notion of Sybil-proofness. Thus, our (im)possibility result does not generalize to the Bayesian setting and we have a larger design space: With Sybil constraints, equivalence between dominant strategy and Bayesian implementation (that holds in classical single-parameter mechanism design without Sybils) no longer holds.

翻译：我们证明，在单参数机制设计环境中，唯一非浪费、对称、激励相容且抗女巫攻击的直接机制是具有对称平局决胜规则的第二价格拍卖。因此，若存在私有信息，则彩票或其他不总是分配给最高出价者的机制要么不抗女巫攻击，要么不满足激励相容性。此外，我们证明了主要（不）可能性结果可推广至线性估值之外的情形，但不适用于投标人存在容量约束的多单位物品分配问题。我们还提供了满足所有其他公理及较弱贝叶斯抗女巫攻击性概念的机制示例（其投标人中期收益高于第二价格拍卖）。因此，我们的（不）可能性结果不能推广至贝叶斯设定，且我们拥有更大的设计空间：在存在女巫攻击约束时，占优策略与贝叶斯实施之间的等价性（在无女巫攻击的经典单参数机制设计中成立）不再成立。