🤖 AI Summary
This paper investigates incentive-compatible mechanism design resilient to Sybil attacks in single-parameter environments. Method: Leveraging axiomatic modeling—specifically non-wastefulness and symmetry—combined with game-theoretic analysis, the authors rigorously characterize Sybil-proof mechanisms. Contribution/Results: The paper establishes, for the first time, the equivalence between Sybil-proofness and incentive compatibility in single-parameter settings. It further proves that the only direct mechanism satisfying non-wastefulness, symmetry, and Sybil-proofness is the second-price auction with symmetric tie-breaking. This result demonstrates the failure of classical mechanism design conclusions under Sybil threats and expands the Bayesian mechanism design space. Moreover, the paper refutes the feasibility of alternative approaches—including randomized allocation—and constructs a high-revenue mechanism satisfying weak Sybil-proofness, thereby breaking the traditional equivalence boundary.
📝 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.