On Sybil Proofness in Competitive Combinatorial Exchanges

TL;DR

This paper analyzes the vulnerability of the BRACE mechanism in combinatorial exchanges to Sybil attacks, establishing bounds on manipulation effects and conditions for strategyproofness.

Contribution

It provides explicit bounds on price and welfare deviations due to Sybil attacks and characterizes when strategyproofness holds in large markets.

Findings

Strategyproofness holds if each principal's identity share vanishes.

Persistent identity shares enable profitable Sybil deviations.

Unbounded Sybil populations make BRACE infeasible without safeguards.

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.