Optimum profit allocation in coalitional VoD service

Although video-on-demand (VoD) services are provided by many ISPs, the amount of content provided by each VoD service is one order smaller than that provided by rental video services, so the limited content count is one of the obstacles to widespread VoD services. To solve this problem, ISPs can form a coalition with other ISPs and use content owned by other ISPs. However, to form a coalition among multiple ISPs, ISPs need to rationally allocate the profit obtained by the coalition to convince all ISPs participating in the coalition. We propose using the Shapley value of the coalitional game as the rational allocation of profit. Assuming that all but one ISP has the same number of users or (and) the same number of rare content, we derive the Shapley value in closed form and clarify the influence of the numbers of users and rare content on the coalition. We also compare the Shapley value with three general allocation models and show that the Shapley value agrees with the allocation when the profit obtained by each content delivery is equally shared by two ISPs, one that accommodates the receiving user and the other that owns the delivered content.