Revenue sharing in network utility maximization problems



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.


Revenue sharing Network utility maximization Alliances Cooperative game theory Stability Efficiency Fairness Monotonicity 


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  1. 1.
    BRITE: Boston Representative Internet Topology Generator [Online] Available:
  2. 2.
    ETICS: Economics and Technologies for Inter-carrier Services. European FP7 Research Project [Online] Available:
  3. 3.
    Amigo, I. (2013). Technological and Economic Aspects for Quality of Service in Multidomain Alliances. Ph.D, thesis.Google Scholar
  4. 4.
    Amigo, I., Belzarena, P., & Vaton, S. (2012). On the problem of revenue sharing in multi-domain federations. In Networking (p. 2012). Czech Republic: Prague.Google Scholar
  5. 5.
    Aumann, R.J., & Shapley, L.S. (1974). Values of non-atomic games. Princeton University Press.Google Scholar
  6. 6.
    Bethanabhotla, D., Caire, G., & Neely, M.J. (2012). Joint transmission scheduling and congestion control for adaptive streaming in wireless device-to-device networks. In Conference record of the 46th Asilomar conference on signals, systems and computers (ASILOMAR), 2012 (pp. 1179–1183). IEEE.Google Scholar
  7. 7.
    Bogomolnaia, A., Holzman, R., & Moulin, H. (2010). Sharing the cost of a capacity network. Mathematics of Operations Research, 35(1), 173–192.CrossRefGoogle Scholar
  8. 8.
    Friedman, E., & Moulin, H. (1999). Three methods to share joint costs or surplus. Journal of Economic Theory, 87(2), 275–312.CrossRefGoogle Scholar
  9. 9.
    Hougaard, J.L. (2009). An introduction to allocation rules. Springer.Google Scholar
  10. 10.
    Kelly, F.P., Maulloo, A.K., & Tan, D.K.H. (1998). Rate control for communication networks: shadow prices, proportional fairness and stability. The Journal of Operational Research Society, 49(3), 237–252.CrossRefGoogle Scholar
  11. 11.
    Moulin, H., & Laigret, F. (2011). Equal-need sharing of a network under connectivity constraints. Games and Economic Behavior, 72(1), 314–320.CrossRefGoogle Scholar
  12. 12.
    Myerson, R.B. (1980). Conference structures and fair allocation rules. International Journal of Game Theory, 9(3), 169–182.CrossRefGoogle Scholar
  13. 13.
    Nash, J.F.J. (1950). The bargaining problem. Econometrica, 18(2), 155–162.CrossRefGoogle Scholar
  14. 14.
    Osborne, M.J., & Rubinstein, A. (1994). A course in game theory, 1st edn. The MIT Press.Google Scholar
  15. 15.
    Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica, 50(1), 97–109.CrossRefGoogle Scholar
  16. 16.
    Rubinstein, A., & Osborne, M.J. (1990). Bargaining and markets. Economic theory, econometrics, and mathematical economics series. San Diego: Academic Press. Notes bibliogr.Google Scholar
  17. 17.
    Samadi, P., Mohsenian-Rad, A.H., Schober, R., Wong, V., & Jatskevich, J. (2010). Optimal real-time pricing algorithm based on utility maximization for smart grid. In First IEEE international conference on smart grid communications (pp. 415–420).Google Scholar
  18. 18.
    Shapley, L. (1953). A value for n-person games. In H. Kuhn, & A. Tucker (Eds.), Contributions to the theory of games, (Vol. 28 pp. 307–317).Google Scholar
  19. 19.
    Shoham, Y., & Leyton-Brown, K. (2009). Multiagent systems: algorithmic, game-theoretic, and logical foundations. Cambridge: Cambridge University Press.Google Scholar
  20. 20.
    Yi, Y., & Chiang, M. (2008). Stochastic network utility maximisation—a tribute to Kelly’s paper published in this journal a decade ago. European Transactions on Telecommunications, 19(4), 421–442.CrossRefGoogle Scholar
  21. 21.
    Young, H. (1985). Monotonic solutions of cooperative games. International Journal of Game Theory, 14, 65–72.CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institut Mines TelecomTélécom BretagneBrest Cedex 3France
  2. 2.Facultad de IngenieríaUniversidad de la RepúblicaMontevideoUruguay

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