Revenue sharing in network utility maximization problems

Abstract

Alliances arise in a wide variety of domains, when a group of countries, political parties, people or other entities agree to work together because of shared interests or aims. They make sense, if the output obtained is somehow better than the outcome of acting individually. Revenue or cost sharing is key when determining if individuals are better off by contributing to an alliance or not. In our alliance each member owns a unique resource –or set of resources–, which is given to the alliance. The alliance sells services, which are supported thanks to one or a set of these resources. We focus on alliances that sell services in such a way that the total revenue of the alliance is maximized. We show that this kind of problems can be modeled through a Network Utility Maximization problem. We subsequently explore the problem of revenue sharing among the members of the alliance. Such a problem is a complex one since the interests of all participants must be ensured and correct incentives must be provided. We formally formulate the members’ interests through a set of properties the revenue sharing method should verify. We then discuss the existing methods for revenue sharing and conclude that none of them verifies the needed properties for the case of a revenue maximizing alliance. We finally propose a revenue sharing method based on projecting the contributions of each member of the alliance into an economic stable set. Through an exhaustive simulative study we conclude that our method provides, in addition to economic stability, fairness among members and the right incentives to them. Through our analysis Network Service Provider alliances, which sell quality-assured data transport services, are considered as an application example.