Tightening Up the Incentive Ratio for Resource Sharing Over the Rings

Fundamental issues in resource sharing over large scale networks have gained much attention from the research community, in response to the growth of sharing economy over the Internet and mobile networks. We are particularly interested in the fundamental file sharing and subsequently P2P network bandwidth sharing developed by BitTorrent and later formalized by Wu and Zhang [15] as the proportional response protocol. It is of practical importance in the design to provide agent incentives to follow the distributed protocol out of their own rationality. We study the robustness of the distributed protocol in this incentive issue against a Sybil attack, a common type of grave threat in P2P network. For the resource sharing on rings, and we characterize the utility gain from a Sybil attack in the concept of incentive ratio. Previous works proved the incentive ratio is lower bounded by two and upper bounded by four, and later the upper bound is improved to three. It has been listed in [5] and [9] as an open problem to tighten them. In this paper, we completely resolve this open problem with a better understanding on the influence from different class agents to the resource allocation under the distributed protocol.