Agent incentives of strategic behavior in resource exchange

In a resource exchange system, resources are shared among multiple interconnected peers. Peers act as both suppliers and customers of resources by making a certain amount of their resources directly available to other network participants. Their utilities are determined by the total amount of resources received from all neighbors. According to a preset mechanism, the allocation of the shared resources depends on the information that agents submit to the mechanism. The participating agents, however, may try to strategically manipulate its submitted information to influence the allocation with the expectation of its utility improvement. In this paper, we consider the tit-for-tat popular proportional response mechanism and discuss the incentives an agent may lie, by a vertex splitting strategy. We apply the concept of incentive ratio to characterize the multiplication factor by which utility of an agent can be increased with the help of the vertex splitting strategy. Because of the bounded rationality in the decentralized resource exchange system, a smaller incentive ratio makes the agents have the less incentive to play strategically. However the incentive ratio is proved to be unbounded in linear exchange market recently. In this paper we focus on the setting on trees, our linear exchange market proves to have the incentive ratio of exact two under the proportional response mechanism against the vertex splitting strategic behaviors of participating agents.