On the stability of ISPs' coalition structure: Shapley value based revenue sharing

The Internet is a complex system, consisting of different economic players in terms of access/transit connection and content distribution, which are typically selfish and try to maximize their own profits. Due to this different perspective of economic interest as well as dynamic changes of the Internet market, a certain degree of techno-economic inefficiency has naturally been observed, e.g., unstable peering and revenue imbalance among content, eyeball, and transit ISPs (Internet Service Providers). At the center of this issue is good revenue sharing among them. Recently, revenue sharing based on the notion of Shapley Value (SV) from cooperative game theory has been applied to address the afore-mentioned issue, shedding light upon many nice properties which have been used not only to understand the current Internet eco-system but also to predict its future. However, the positive features from the SV based revenue sharing can be practically feasible only when the providers agree to form a grand coalition, which may not hold in practice. In this paper, we first investigate the conditions under which the grand coalition is stable under SV by classifying the network into two cases: under-demanded and over-demanded. We then study the gap between the conditions of the grand coalition's stability and optimal coalition structures (i.e., coalition structures that maximize the aggregate revenue of ISPs).