Incentive Ratios of a Proportional Sharing Mechanism in Resource Sharing

In a resource sharing system, resources are shared among multiple interconnected peers. Peers act as both suppliers and customers of resources by making a certain amount of their resource directly available to others. In this paper we focus on a proportional sharing mechanism, which is fair, efficient and guarantees a market equilibrium in the resource sharing system. We study the incentives an agent may manipulate such a mechanism, by the vertex splitting strategy, for personal gains and adopt a concept called incentive ratio to quantify the amount of gains. For the resource sharing system where the underlying network ia a cycle, we prove that the incentive ratio on this kind of network is bounded by 2 ≤ ζ ≤ 4. Furthermore, the incentive ratio on an even cycle, a cycle with even number of vertices, is proved to be exactly 2.