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On Sybil-proof Mechanisms

Minghao Pan, Bruno Mazorra, Christoph Schlegel, Akaki Mamageishvili

TL;DR

This paper establishes a sharp impossibility for Sybil-proof mechanisms in the classical single-parameter mechanism design setting: any non-wasteful, symmetric, and dominant-strategy incentive compatible mechanism that is immune to a single Sybil attack must be a second-price auction with symmetric tie-breaking. The authors extend the analysis to Bayesian settings, showing that relaxing to Bayesian Sybil-proofness yields additional mechanisms that do not always allocate to the highest bidder, thus widening the design space under Sybil constraints. They formalize a Revelation Principle for Sybils and demonstrate that the dominance of second-price rules hinges on the strong ex-post requirements. Extensions show the impossibility does not automatically generalize to multi-unit or unit-demand settings, and that with type-convex valuations and superadditive interim utility the generalized second-price mechanism remains the unique solution under their axioms. Overall, the work clarifies the trade-offs between Sybil-resistance, allocation efficiency, and robustness of implementation in mechanism design, and highlights new avenues in Bayesian and approximate implementations.

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.

On Sybil-proof Mechanisms

TL;DR

This paper establishes a sharp impossibility for Sybil-proof mechanisms in the classical single-parameter mechanism design setting: any non-wasteful, symmetric, and dominant-strategy incentive compatible mechanism that is immune to a single Sybil attack must be a second-price auction with symmetric tie-breaking. The authors extend the analysis to Bayesian settings, showing that relaxing to Bayesian Sybil-proofness yields additional mechanisms that do not always allocate to the highest bidder, thus widening the design space under Sybil constraints. They formalize a Revelation Principle for Sybils and demonstrate that the dominance of second-price rules hinges on the strong ex-post requirements. Extensions show the impossibility does not automatically generalize to multi-unit or unit-demand settings, and that with type-convex valuations and superadditive interim utility the generalized second-price mechanism remains the unique solution under their axioms. Overall, the work clarifies the trade-offs between Sybil-resistance, allocation efficiency, and robustness of implementation in mechanism design, and highlights new avenues in Bayesian and approximate implementations.

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.
Paper Structure (16 sections, 15 theorems, 99 equations)

This paper contains 16 sections, 15 theorems, 99 equations.

Table of Contents

  1. Introduction
  2. Related Work and Implications
  3. Model and Result
  4. The Revelation Principle for Sybils
  5. Characterization Result
  6. Bayesian Sybil-Proofness
  7. Extensions
  8. Multiple Goods with Unit-Demand
  9. Super-additive Utility
  10. Conclusion
  11. Revelation principle
  12. Sybil-Proofness of Example 1
  13. Lemmas for the Proof of Theorem \ref{['thm:general']}
  14. Proof of Lemma \ref{['lemma:monotone']}
  15. Proof of Proposition \ref{['MultiUnit']}
  16. ...and 1 more sections

Key Result

Theorem 1

A direct mechanism is payment normalized, non-wasteful, symmetric, incentive compatible, and Sybil-proof if and only if it is a second price auction with symmetric tie-breaking.

Theorems & Definitions (32)

  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Example 1
  • Example 2
  • ...and 22 more