Abstract
We study influence maximization problems over social networks, in the presence of competition. Our focus is on diffusion processes within the family of threshold models. Motivated by the general lack of positive results establishing monotonicity and submodularity of the influence function for threshold models, we introduce a general class of switching-selection threshold models where the switching and selection functions may also depend on the node activation history. This extension allows us to establish monotonicity and submodularity when (i) the switching function is linear and depends on the influence by all active neighbors, and (ii) the selection function is linear and depends on the influence by the nodes activated only in the last step. This implies a (1 − 1/e − ε)-approximation for the influence maximization problem in the competitive setting. On the negative side, we present a collection of counterexamples establishing that the restrictions above are essentially necessary. Moreover, we show that switching-selection threshold games with properties (i) and (ii) are valid utility games, and thus their Price of Anarchy is at most 2.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
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)
Domingos, P., Richardson, M.: Mining the network value of customers. In: KDD 2001, pp. 57–66.
Goldenberg, J., Libai, B., Muller, E.: Talk of the network: A complex systems look at the underlying process of word-of-mouth. Marketing Letters, 211–223 (2001)
Goyal, S., Kearns, M.: Competitive contagion in networks. In: STOC 2012, pp. 759–774 (2012)
Granovetter, M.S.: Threshold models of collective behavior. The American Journal of Sociology, 1420–1443 (1978)
He, X., Kempe, D.: Price of anarchy for the N-player competitive cascade game with submodular activation functions. In: Chen, Y., Immorlica, N. (eds.) WINE 2013. LNCS, vol. 8289, pp. 232–248. Springer, Heidelberg (2013)
Kapralov, M., Post, I., Vondrák, J.: Online submodular welfare maximization: Greedy is optimal. In: SODA 2013, pp. 1216–1225 (2013)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: KDD 2003, pp. 137–146 (2013)
Mossel, E., Roch, S.: Submodularity of influence in social networks: From local to global. SIAM J. Comput., 2176–2188 (2010)
Nemhauser, G.L., Wolsey, L.A., Fisher, M.L.: An analysis of approximations for maximizing submodular set functions. Mathematical Programming, 265–294
Schelling, T.C.: Micromotives and Macrobehavior (1978)
Vetta, A.: Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions. In: FOCS 2002, pp. 416–425 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fotakis, D., Lykouris, T., Markakis, E., Obraztsova, S. (2014). Influence Maximization in Switching-Selection Threshold Models. In: Lavi, R. (eds) Algorithmic Game Theory. SAGT 2014. Lecture Notes in Computer Science, vol 8768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44803-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-662-44803-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44802-1
Online ISBN: 978-3-662-44803-8
eBook Packages: Computer ScienceComputer Science (R0)