Equilibrium Flows and Path Dilation for a Network Forwarding Game

Abstract

We consider a forwarding game on directed graphs where selfish nodes need to send certain amount of flow (packets) to specific destinations, possibly through several relay nodes. Each node has to decide whether to pay the cost of relaying flow as an intermediate node, given the fact that its neighbors can punish it for its non-cooperation. In this work we simplify the original network model, and provide the first experimental evaluation of these equilibria for different classes of graphs. We provide clear evidence that these equilibrium solutions are indeed significant and establish how these equilibria depend on various properties of the network such as average degrees and flow demand density. Our main results establish experimental bounds for the path dilation in this model: the average ratio of the routed flow cost at equilibrium over the cost of the optimal routing which would involve shortest path routing in our model.