On Sybil-proof Mechanisms

Minghao Pan; Bruno Mazorra; Christoph Schlegel; Akaki Mamageishvili

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arXiv · 2407.14485

On Sybil-proof Mechanisms

Minghao Pan·Bruno Mazorra·Christoph Schlegel·Akaki Mamageishvili

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Abstract

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.

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Minghao Pan, Bruno Mazorra, Christoph Schlegel, Akaki Mamageishvili. 2024-07-19. On Sybil-proof Mechanisms. https://arxiv.org/abs/2407.14485

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