Tight Incentive Analysis on Sybil Attacks to Market Equilibrium of Resource Exchange over General Networks

Abstract

The Internet-scale peer-to-peer (P2P) systems usually build their success on distributed protocols. For example, the well-known BitTorrent network for resource exchange is based on the proportional response protocol, where each participant exchanges its resources with its neighbors in proportion to what it has received in the previous round. The dynamics of such a protocol has been proved to converge to a market equilibrium. On the other hand, it requires thorough incentive analysis to show the robustness of such protocol, as the distributed agents may strategically manipulate the system once they are able to benefit. Recent studies have developed strategyproofness results of the proportional response protocol against agent deviations in the forms of weight cheating and edge deleting. However, the protocol is not truthful against Sybil attacks, under which an agent may create several fictitious identities and control these fictitious identities to exchange resources with others. In this paper, we apply the concept of incentive ratio to measure how much the utility of a strategic agent in a market equilibrium can be improved by playing Sybil attacks. We prove a tight incentive ratio of two for any agent launching Sybil attacks over general networks. The tight incentive ratio of two closes an open problem modeling the successful tit-for-tat protocol for Internet resource exchanging and also presents a complete picture in this line of theoretical studies with real applications.