A Game-Theoretic Analysis of a Competitive Diffusion Process over Social Networks

  • Vasileios Tzoumas
  • Christos Amanatidis
  • Evangelos Markakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)


We study a game-theoretic model for the diffusion of competing products in social networks. Particularly, we consider a simultaneous non-cooperative game between competing firms that try to target customers in a social network. This triggers a competitive diffusion process, and the goal of each firm is to maximize the eventual number of adoptions of its own product. We study issues of existence, computation and performance (social inefficiency) of pure strategy Nash equilibria in these games. We mainly focus on 2-player games, and we model the diffusion process using the known linear threshold model. Nonetheless, many of our results continue to hold under a more general framework for this process.


Social Network Nash Equilibrium Congestion Game Game Matrix Pure Nash Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alon, N., Feldman, M., Procaccia, A.D., Tennenholtz, M.: A note on competitive diffusion through social networks. Information Processing Letters (IPL) 110(6), 221–225 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Apt, K.R., Markakis, E.: Diffusion in Social Networks with Competing Products. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 212–223. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Bharathi, S., Kempe, D., Salek, M.: Competitive Influence Maximization in Social Networks. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 306–311. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Borodin, A., Filmus, Y., Oren, J.: Threshold Models for Competitive Influence in Social Networks. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 539–550. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Carnes, T., Nagarajan, C., Wild, S.M., van Zuylen, A.: Maximizing influence in a competitive social network: A follower’s perspective. In: 9th International Conference on Electronic Commerce (ICEC), pp. 351–360 (2007)Google Scholar
  6. 6.
    Chen, N.: On the approximability of influence in social networks. SIAM Journal on Discrete Mathematics (SIDMA) 23(3), 1400–1415 (2009)zbMATHCrossRefGoogle Scholar
  7. 7.
    Chien, S., Sinclair, A.: Convergence to approximate Nash equilibria in congestion games. Games and Economic Behavior 71(2), 315–327 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Domingos, P., Richardson, M.: Mining the network value of customers. In: 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 57–66 (2001)Google Scholar
  9. 9.
    Goldenberg, J., Libai, B., Muller, E.: Talk of the network: A complex systems look at the underlying process of word-of-mouth. Marketing Letters 12(3), 211–223 (2001)CrossRefGoogle Scholar
  10. 10.
    Goyal, S., Kearns, M.: Competitive contagion in networks. In: 44th ACM Symposium on Theory of Computing (STOC), pp. 759–774 (2012)Google Scholar
  11. 11.
    Granovetter, M.S.: Threshold models of collective behavior. The American Journal of Sociology 83(6), 1420–1443 (1978)CrossRefGoogle Scholar
  12. 12.
    Immorlica, N., Kleinberg, J., Mahdian, M., Wexler, T.: The role of compatibility in the diffusion of technologies through social networks. In: Proceedings of the 8th ACM Conference on Electronic Commerce (EC), pp. 75–83 (2007)Google Scholar
  13. 13.
    Kempe, D., Kleinberg, J., Tardos, E.: Maximizing the spread of influence in a social network. In: 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 137–146 (2003)Google Scholar
  14. 14.
    Kostka, J., Oswald, Y.A., Wattenhofer, R.: Word of Mouth: Rumor Dissemination in Social Networks. In: Shvartsman, A.A., Felber, P. (eds.) SIROCCO 2008. LNCS, vol. 5058, pp. 185–196. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Leskovec, J., Adamic, L., Huberman, B.: The dynamics of viral marketing. ACM Transactions on the Web (TWEB) 1(1), Article No. 5 (2007)Google Scholar
  16. 16.
    Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14, 124–143 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Morris, S.: Contagion. The Review of Economic Studies 67(1), 57–78 (2000)zbMATHCrossRefGoogle Scholar
  18. 18.
    Mossel, E., Roch, S.: On the submodularity of influence in social networks. In: Symposium on Theory of Computing (STOC), pp. 128–134 (2007)Google Scholar
  19. 19.
    Schelling, T.C.: Micromotives and Macrobehavior. Norton, New York (1978)Google Scholar
  20. 20.
    Simon, S., Apt, K.R.: Choosing products in social networks (2012) (manuscript),
  21. 21.
    Takehara, R., Hachimori, M., Shigeno, M.: A comment on pure-strategy Nash equilibria in competitive diffusion games. Information Processing Letters (IPL) 112(3), 59–60 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vasileios Tzoumas
    • 1
    • 3
  • Christos Amanatidis
    • 2
  • Evangelos Markakis
    • 2
  1. 1.School of Electrical and Computer EngineeringNational Technical University of AthensGreece
  2. 2.Department of InformaticsAthens University of Economics and BusinessGreece
  3. 3.Department of Electrical and Systems EngineeringUniversity of PennsylvaniaUSA

Personalised recommendations