Incentivizing Hosts via Multilateral Cooperation in User-Provided Networks: A Fluid Shapley Value Approach

Successful operation of User-Provided Networks (UPN) requires that both of Internet Service Provider (ISP) and self network-operating users (hosts) cooperate appropriately in terms of resource sharing and pricing strategy since ISP and hosts have a multilateral reliance on each other with respect to virtual infrastructure expansion and Internet connectivity. However, it has been underexplored whether such cooperation provides sufficient incentive to ISP and hosts under a setup where ISP and hosts are fully included, having a high dependence on how to cooperate and how to distribute the resulting cooperation worth. In this paper, we model a market of UPN, consisting of ISP, hosts, and clients via game theory, where we model various heterogeneities in terms of (i) willingness to pay and mobility pattern of clients, (ii) hosts' QoS, and (iii) type of cooperation among ISP and hosts. The key technical challenges lie in the natural mixture of cooperative and non-cooperative game theoretic angles, where the worth function---one of the crucial components in coalitional game theory---comes from the equilibrium of an embedded, non-cooperative two-stage dynamic game. We consider the Shapley value as a mechanism of revenue sharing and overcome its hardness in characterization by taking the fluid limit when the number of hosts and clients is large. Our analytical studies reveal useful implications that in UPN when and how much economic benefits can be given to the players and when they maintain their grand coalition under what conditions, referred to as stability.