From Local Network Formation Game to Peer-to-Peer Protocol

Peer-to-peer protocols often take longer, are less efficient or can't complete lookup queries with increasing network diameter. Peers could mitigate this by increasing their degree, i.e., their amount of open connections, but this increases the operational cost for each peer.

We propose a novel peer-to-peer network formation protocol based on a game-theoretic approach, guaranteeing that diameter and maximum degree do not surpass given thresholds throughout the network. The game generalizes the local network formation game with more versatile strategies and cost functions. This allows for a trade off between operational cost and efficiency based on the individual interest of peers.

We show that for any given diameter k and maximum degree d a Nash equilibrium, i.e., a graph with the desired properties, can be reached by improvement steps. We validate the practical applicability of these theoretical results on networks of 5–50 participants with various strategies and configurations. The experimental results show a fast approximation of the desired properties while taking some time to reach a stable state. We make out several strategies with which the protocol performs well. In particular, a stable state is found quickly when the initial network was already close to a stable state. This property enables the efficient dynamic treatment of the in practice often occurring scenario of nodes joining or leaving the network.