Topological influence on optimality of Tit-for-Tat based P2P content distribution

Peer-to-Peer (P2P) content distribution is a powerful scheme to distribute content on the Internet. Since the P2P content distribution relies on the cooperation among peers, one of the most famous P2P file distribution systems, BitTorrent, has applied a game theoretical approach called the Tit-for-Tat (TFT) strategy to encourage selfish peers to cooperatively exchange the fragments of a file, i.e., pieces, with others. In recent years, the basic characteristics of such TFT-based P2P content distribution under a full-mesh network has been investigated by modeling the determination of the optimal piece flow as Integer Linear Programming (ILP). However, the topological influence on optimal piece flow has not been revealed yet. In this paper, we propose an approach to analyze the topological influence by extending the previous model. Through numerical results, we reveal that the optimal piece flow can be achieved on a hierarchical and circular topology with O(NP) links where NP is the number of peers. We also show the whole network can be divided into multiple sub-networks while keeping the system performance.