On Sybil-proof Mechanisms

TL;DR

This paper proves that in single-parameter environments, the second price auction is uniquely Sybil-proof, incentive compatible, and non-wasteful, highlighting limitations of other mechanisms and extending the impossibility results beyond linear valuations.

Contribution

It establishes a fundamental uniqueness result for Sybil-proof mechanisms in single-parameter settings and explores the boundaries of these results beyond linear valuations and in Bayesian contexts.

Findings

Second price auction is the only non-wasteful, symmetric, incentive compatible, Sybil-proof mechanism.

Lotteries and other mechanisms are not Sybil-proof or incentive compatible in private information settings.

The impossibility result does not extend to Bayesian settings, allowing for more mechanism options.

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.