Tight incentive analysis of Sybil attacks against the market equilibrium of resource exchange over general networks

The BitTorrent network, a well-known Internet-scale P2P system, applies the proportional response protocol to exchange resource, where each participant contributes resource to neighbors in proportion to the amount it received in the previous round. The dynamics of this protocol is known to converge to a market equilibrium. However, an agent may manipulate this protocol by a Sybil attack to create fictitious identities and control them to gain more benefit. We apply the concept of incentive ratio, the percentage of the new utility after a Sybil attack over the benchmark, to measure the incentive of a strategic agent to play a Sybil attack, proving a tight bound of two over general networks. This finding completes the theoretical picture for incentive analysis on Sybil attacks facing the legendary tit-for-tat protocol for Internet bandwidth sharing and other applications.