A Dynamics for Advertising on Networks

  • L. Elisa CelisEmail author
  • Mina Dalirrooyfard
  • Nisheeth K. Vishnoi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10660)


We study the following question facing businesses in the world of online advertising: how should an advertising budget be spent when there are competing products? Broadly, there are two primary modes of advertising: (i) the equivalent of billboards in the real-world and (search or display) ads online that convert a percentage of the population that sees them, and (ii) social campaigns where the goal is to select a set of initial adopters who influence others to buy via their social network. Prior work towards the above question has largely focused on developing models to understand the effect of one mode or the other. We present a stochastic dynamics to model advertising in social networks that allows both and incorporates the three primary forces at work in such advertising campaigns: (1) the type of campaign – which can combine buying ads and seed selection, (2) the topology of the social network, and (3) the relative quality of the competing products. This model allows us to study the evolution of market share of multiple products with different qualities competing for the same set of users, and the effect that different advertising campaigns can have on the market share. We present theoretical results to understand the long-term behavior of the parameters on the market share and complement them with empirical results that give us insights about the, harder to mathematically understand, short-term behavior of the model.


  1. 1.
    Bass, F.M.: A new product growth model for consumer durables. Manag. Sci. 15(5), 215–227 (1969)CrossRefzbMATHGoogle Scholar
  2. 2.
    Benaïm, M.: Dynamics of stochastic approximation algorithms. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds.) Séminaire de Probabilités XXXIII. LNM, vol. 1709, pp. 1–68. Springer, Heidelberg (1999). CrossRefGoogle Scholar
  3. 3.
    Van den Bulte, C., Joshi, Y.V.: New product diffusion with influentials and imitators. Mark. Sci. 26(3), 400–421 (2007)CrossRefGoogle Scholar
  4. 4.
    Chazelle, B.: The dynamics of influence systems. In: 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science (FOCS), pp. 311–320. IEEE (2012)Google Scholar
  5. 5.
    Díaz, J., Goldberg, L.A., Mertzios, G.B., Richerby, D., Serna, M., Spirakis, P.G.: Approximating fixation probabilities in the generalized moran process. Algorithmica 69(1), 78–91 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Dixit, N., Srivastava, P., Vishnoi, N.K.: A finite population model of molecular evolution: theory and computation. J. Comput. Biol. 19(10), 1176–1202 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Easley, D., Kleinberg, J.: Networks, Crowds, and Markets. Cambridge University Press, Cambridge (2010)CrossRefzbMATHGoogle Scholar
  8. 8.
    Efthymiou, C., Hayes, T.P., Stefankovic, D., Vigoda, E., Yin, Y.: Convergence of MCMC and loopy BP in the tree uniqueness region for the hard-core model. In: IEEE 57th Annual Symposium on Foundations of Computer Science, FOCS 2016, 9–11 October 2016, Hyatt Regency, New Brunswick, New Jersey, USA, pp. 704–713 (2016).
  9. 9.
    Galeotti, A., Goyal, S.: Influencing the influencers: a theory of strategic diffusion. RAND J. Econ. 40(3), 509–532 (2009)CrossRefGoogle Scholar
  10. 10.
    Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978)CrossRefGoogle Scholar
  11. 11.
    Herr, P.M., Kardes, F.R., Kim, J.: Effects of word-of-mouth and product-attribute information on persuasion: an accessibility-diagnosticity perspective. J. Consum. Res. 17(4), 454–462 (1991)CrossRefGoogle Scholar
  12. 12.
    Hinz, O., Skiera, B., Barrot, C., Becker, J.U.: Seeding strategies for viral marketing: an empirical comparison. J. Mark. 75(6), 55–71 (2011)CrossRefGoogle Scholar
  13. 13.
    Iyer, G., Soberman, D., Villas-Boas, J.M.: The targeting of advertising. Mark. Sci. 24(3), 461–476 (2005)CrossRefGoogle Scholar
  14. 14.
    Jain, D., Mahajan, V., Muller, E.: An approach for determining optimal product sampling for the diffusion of a new product. J. Prod. Innov. Manag. 12(2), 124–135 (1995)CrossRefGoogle Scholar
  15. 15.
    Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: The 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 137–146. ACM (2003)Google Scholar
  16. 16.
    Leskovec, J., Krevl, A.: SNAP Datasets, June 2014.
  17. 17.
    Lieberman, E., Hauert, C., Nowak, M.A.: Evolutionary dynamics on graphs. Nature 433(7023), 312–316 (2005)CrossRefGoogle Scholar
  18. 18.
    Lohtia, R., Donthu, N., Hershberger, E.K.: The impact of content and design elements on banner advertising click-through rates. J. Advertising Res. 43(04), 410–418 (2003)CrossRefGoogle Scholar
  19. 19.
    Marsden, P.V., Friedkin, N.E.: Network studies of social influence. Sociol. Methods Res. 22(1), 127–151 (1993)CrossRefGoogle Scholar
  20. 20.
    Nowak, M.A.: Evolutionary Dynamics. Harvard University Press, Cambridge (2006)zbMATHGoogle Scholar
  21. 21.
    Palmeri, C.: Online ad spending to pass tv spots this year, consultant says (2015).
  22. 22.
    Palmeri, C.: Social network ad spending to hit $23.68 billion worldwide (2015).
  23. 23.
    Pemantle, R.: When are touchpoints limits for generalized pólya urns? Proc. Am. Math. Soc. 113, 235–243 (1991)zbMATHGoogle Scholar
  24. 24.
    Schelling, T.C.: Micromotives and Macrobehavior. WW Norton and Company, New York City (1978)Google Scholar
  25. 25.
    Scott, D.M.: The New Rules of Marketing and PR: How to Use Social Media, Online Video, Mobile Applications, Blogs, News Releases, and Viral Marketing to Reach Buyers Directly. John Wiley and Sons, Hoboken (2013)Google Scholar
  26. 26.
    Shy, O.: The Economics of Network Industries. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  27. 27.
    Tripathi, K., Balagam, R., Vishnoi, N.K., Dixit, N.M.: Stochastic simulations suggest that HIV-1 survives close to its error threshold. PLoS Comput. Biol. 8(9), e1002684 (2012)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Vishnoi, N.K.: The speed of evolution. In: Symposium on Discrete Algorithms (SODA), pp. 1590–1601 (2015)Google Scholar
  29. 29.
    Vranica, S.: IBM pours $100 million into ad consulting (2014).
  30. 30.
    Weaver, O.: How to set social advertising goals (2015).
  31. 31.
    Wormald, N.C.: Differential equations for random processes and random graphs. Ann. Appl. Probab. 5(4), 1217–1235 (1995)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • L. Elisa Celis
    • 1
    Email author
  • Mina Dalirrooyfard
    • 2
  • Nisheeth K. Vishnoi
    • 1
  1. 1.École Polytechnique Fédérale de Lausanne (EPFL)LausanneSwitzerland
  2. 2.Massachusetts Institute of Technology (MIT)CambridgeUSA

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