On Sybil Proofness in Competitive Combinatorial Exchanges
Abhimanyu Nag
TL;DR
This work analyzes Sybil manipulation in BRACE, a budget-relaxed competitive equilibrium for combinatorial exchanges, by treating identity creation as perturbations of the reported type distribution. It proves linear bounds: small Sybil invasions induce $O(\alpha)$ price and welfare deviations under local regularity, and sublinear principal gains vanish only when every principal's identity share tends to zero. A sharp dichotomy shows principal-level strategyproofness in the large holds if and only if identity dispersion eliminates influence; otherwise, non-vanishing shares enable profitable deviations. It also shows BRACE cannot exist under unbounded Sybil mass and provides a design inequality linking Sybil-deterrence costs to both per-identity misreport gains and price-impact effects, offering concrete guidance for Sybil-resistant deployment in large markets.
Abstract
We study Sybil manipulation in BRACE, a competitive equilibrium mechanism for combinatorial exchanges, by treating identity creation as a finite perturbation of the empirical distribution of reported types. Under standard regularity assumptions on the excess demand map and smoothness of principal utilities, we obtain explicit linear bounds on price and welfare deviations induced by bounded Sybil invasion. Using these bounds, we prove a sharp contrast: strategyproofness in the large holds if and only if each principal's share of identities vanishes, whereas any principal with a persistent positive share can construct deviations yielding strictly positive limiting gains. We further show that the feasibility of BRACE fails in the event of an unbounded population of Sybils and provide a precise cost threshold that ensures disincentivization of such attacks in large markets.