Impact of Social Network Structure on Social Welfare and Inequality

Part of the Studies in Computational Intelligence book series (SCI, volume 526)


In this chapter, how the structure of a network can affect the social welfare and inequality (measured by the Gini coefficient) are investigated based on a graphical game model which is referred to as the Networked Resource Game (NRG). For the network structure, the Erdos–Renyi model, the preferential attachment model, and several other network structure models are implemented and compared to study how these models can effect the game dynamics. We also propose an algorithm for finding the bilateral coalition-proof equilibria because Nash equilibria do not lead to reasonable outcomes in this case. In economics, increasing inequalities and poverty can be sometimes interpreted as a circular cumulative causations, such positive feedback is also considered by us and a modified version of the NRG by considering the positive feedback (p-NRG) is proposed. The influence of network structures in this new model is also discussed at the end of this chapter.


Networked resource game P-NRG network formation Graphical games Nash equilibrium 



This research is partly funded by the NCET Program, Ministry of Education, China, and the National Natural Science Foundation of China (NSFC) under Grant No. 61305047.


  1. 1.
    Albert, R., Barabasi, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)Google Scholar
  2. 2.
    Axelrod, R., Hamilton, W.D.: The evolution of cooperation. Science 211, 1390–1396 (1981)Google Scholar
  3. 3.
    Bowling, M.: Convergence and no-regret in multiagent learning. In: Advances in Neural Information Processing Systems 17 (NIPS), pp. 209–216, 2005. A longer version is available as a University of Alberta Technical Report, TR04-11Google Scholar
  4. 4.
    Duong, Q., Vorobeychik, Y., Singh, S., Wellman, M.P.: Learning graphical game models. In: IJCAI (2011)Google Scholar
  5. 5.
    Elkind, E., Goldberg, L., Goldberg, P.: Nash equilibria in graphical games on trees revisited. In: Proceedings of the 7th ACM Conference on Electronic Commerce, pp. 100–109. ACM, New York (2006)Google Scholar
  6. 6.
    Erdo, P., Renyi, A.: On random graphs. Mathematicae 6, 290–297 (1959)Google Scholar
  7. 7.
    Gini, C.: On the measure of concentration with special reference to income and statistics. Colorado College Publication (1936)Google Scholar
  8. 8.
    Greenwald, A., Hall, K.: Correlated q-learning. In: 20th International Conference on Machine Learning, pp. 242–249 (2003)Google Scholar
  9. 9.
    Groh, G., Lehmann, A., Reimers, J., Friess, M., Schwarz, L.: Detecting social situations from interaction geometry. In: 2010 IEEE Second International Conference on Social Computing (SocialCom), pp. 1–8 (2010)Google Scholar
  10. 10.
    Heckerman, D., Geiger, D., Chickering, D.M.: Learning bayesian networks: the combination of knowledge and statistical data. In: Machine Learning, pp. 197–243 (1995)Google Scholar
  11. 11.
    Hsieh, H.-P., Li, C.-T.: Mining temporal subgraph patterns in heterogeneous information networks. In: 2010 IEEE Second International Conference on Social Computing (SocialCom), pp. 282–287 (2010)Google Scholar
  12. 12.
    Irving, R.W.: An efficient algorithm for the stable roommates problem. J. Algorithms. 6(4), 577–595 (1985)Google Scholar
  13. 13.
    Jackson, M.O.: Allocation rules for network games. Games Econ. Behav. 51(1), 128–154 (2005)Google Scholar
  14. 14.
    Jackson, M.O., Watts, A.: The evolution of social and economic networks. J. Econ. Theor. 106(2), 265–295 (2002)Google Scholar
  15. 15.
    Kakhbod, A., Teneketzis, D.: Games on social networks: on a problem posed by goyal. CoRR. abs/1001.3896 (2010)Google Scholar
  16. 16.
    Kearns, M., Littman, M., Singh, S.: Graphical models for game theory. In: Conference on Uncertainty in Artificial Intelligence, pp. 253–260 (2001)Google Scholar
  17. 17.
    E. Kim, L. Chi, R. Maheswaran, and Y.-H. Chang. Dynamics of behavior in a network game. In IEEE International Conference on Social Computation (2011)Google Scholar
  18. 18.
    Li, Z., Chang, Y.-H., Maheswaran, R.T.: Graph formation effects on social welfare and inequality in a networked resource game. In: SBP, pp. 221–230 (2013)Google Scholar
  19. 19.
    Luca, M.D., Cliff, D.: Human-agent auction interactions: adaptive-aggressive agents dominate. In: IJCAI (2011)Google Scholar
  20. 20.
    Luo, L., Chakraborty, N., Sycara, K.: Prisoner’s dilemma in graphs with heterogeneous agents. In: 2010 IEEE Second International Conference on Social Computing (SocialCom), pp. 145–152 (2010)Google Scholar
  21. 21.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V. (eds.): Algorithmic Game Theory. Cambridge University Press, New York (2007)Google Scholar
  22. 22.
    Ortiz, L., Kearns, M.: Nash propagation for loopy graphical games. In: Neural Information Processing Systems (2003)Google Scholar
  23. 23.
    Erdos, P., Renyi, A.: On random graphs. Publicationes Mathematicae 6, 290–297 (1959)Google Scholar
  24. 24.
    Qiu, B., Ivanova, K., Yen, J., Liu, P.: Behavior evolution and event-driven growth dynamics in social networks. In: 2010 IEEE Second International Conference on Social Computing (SocialCom), pp. 217–224 (2010)Google Scholar
  25. 25.
    Shoham, Y.: Computer science and game theory. Commun. ACM 51(8), 74–79 (2008)Google Scholar
  26. 26.
    Vickrey, D., Koller, D.: Multi-agent algorithms for solving graphical games. In: National Conference on Artificial Intelligence (AAAI) (2002)Google Scholar
  27. 27.
    von Neumann J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)Google Scholar
  28. 28.
    Wani, M.A., Li, T., Kurgan, L.A., Ye, J., Liu, Y. (eds.): In: The Fifth International Conference on Machine Learning and Applications, ICMLA 2006, Orlando, Florida, USA, 14–16 December 2006. IEEE Computer Society (2006)Google Scholar
  29. 29.
    Yang, X.-S. (ed.): Artificial Intelligence, Evolutionary Computing and Metaheuristics—In the Footsteps of Alan Turing, Studies in Computational Intelligence. vol. 427, Springer, Berlin (2013)Google Scholar
  30. 30.
    Yitzhaki, S.: More than a dozen alternative ways of spelling gini economic inequality. Econ. Inequality 8, 13–30 (1998)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Intelligent Computing and Machine Learning Lab, School of Automation Science and Electrical EngineeringBeihang UniversityBeijingChina

Personalised recommendations