Abstract
Viral marketing takes advantage of preexisting social networks among customers to achieve large changes in behaviour. Models of influence spread have been studied in a number of domains, including the effect of “word of mouth” in the promotion of new products or the diffusion of technologies. A social network can be represented by a graph where the nodes are individuals and the edges indicate a form of social relationship. The flow of influence through this network can be thought of as an increasing process of active nodes: as individuals become aware of new technologies, they have the potential to pass them on to their neighbours. The goal of marketing is to trigger a large cascade of adoptions. In this paper, we develop a mathematical model that allows to analyze the dynamics of the cascading sequence of nodes switching to the new technology. To this end we describe a continuous-time and a discrete-time models and analyse the proportion of nodes that adopt the new technology over time.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Balogh, J., Pittel, B.G.: Bootstrap percolation on the random regular graph. Random Structures Algorithms 30(1-2), 257–286 (2007)
Domingos, P., Richardson, M.: Mining the network value of customers. In: KDD 2001: Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 57–66. ACM Press, New York (2001)
Galeotti, A., Goyal, S., Jackson, M.O., Vega-Redondo, F., Yariv, L.: Network games (2007)
Ganesh, A., Massoulié, L., Towsley, D.: The effect of network topology on the spread of epidemics. In: Proceedings IEEE Infocom (2005)
Jackson, M.O., Yariv, L.: Diffusion of behavior and equilibrium properties in network games. American Economic Review (Papers and Proceedings) 97(2), 92–98 (2007)
Janson, S., Łuczak, T., Rucinski, A.: Random graphs. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley Interscience, New York (2000)
Kleinberg, J.: Cascading behavior in networks: Algorithmic and economic issues. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)
Lelarge, M.: Diffusion and cascading behavior in random networks (in preparation)
Lelarge, M.: Diffusion of innovations on random networks: Understanding the chasm. In: Papadimitriou, C.H., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 178–185. Springer, Heidelberg (2008)
Mahajan, V., Muller, E., Bass, F.M.: New product diffusion models in marketing: A review and directions for research. Journal of Marketing 54(1), 1–26 (1990)
Maniatis, P., Roussopoulos, M., Giuli, T., Rosenthal, D.S.H., Baker, M.: The lockss peer-to-peer digital preservation system. ACM Transactions on Computer Systems 23 (2005)
Morris, S.: Contagion. Rev. Econom. Stud. 67(1), 57–78 (2000)
van der Hofstad, R.: Random graphs and complex networks (2008), http://www.win.tue.nl/~rhofstad/NotesRGCN2008.pdf
Watts, D.: A simple model of global cascades on random networks. Proceedings of the National Academy of Science 99, 5766–5771 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Amini, H., Draief, M., Lelarge, M. (2009). Marketing in a Random Network. In: Altman, E., Chaintreau, A. (eds) Network Control and Optimization. NET-COOP 2008. Lecture Notes in Computer Science, vol 5425. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00393-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-00393-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00392-9
Online ISBN: 978-3-642-00393-6
eBook Packages: Computer ScienceComputer Science (R0)