Influence propagation in adversarial setting: how to defeat competition with least amount of investment

It has been observed that individuals' decisions to adopt a product or innovation are often influenced by the recommendations of their friends and acquaintances. Motivated by this observation, the last few years have seen a number of studies on influence maximization in social networks. The primary goal of these studies is identification of k most influential nodes in a network. A major limitation of these studies is that they focus on a non-adversarial environment, where only one player is engaged in influencing the nodes. However, in a realistic scenario multiple players attempt to influence the nodes in a competitive fashion. The proposed model considers a competitive environment where a node that has not yet adopted an innovation, can adopt only one of the several competing innovations and once it adopts an innovation, it does not switch. The paper studies the scenario where the first player has already chosen a set of k nodes and the second player, with the knowledge of the choice of the first, attempts to identify a smallest set of nodes (excluding the ones already chosen by the first) so that when the influence propagation process ends, the number of nodes influenced by the second player is larger than the number of nodes influenced by the first. The paper studies two propagation models and shows that in both the models, the identification of the smallest set of nodes to defeat the adversary is NP-Hard. It provides an approximation algorithm and proves that the performance bound is tight. It also presents the results of extensive experimentation using the collaboration network data. Experimental results show that the second player can easily defeat the first with this algorithm, if the first utilizes the node degree or closeness centrality based algorithms for the selection of influential nodes. The proposed algorithm also provides better performance if the second player utilizes it instead of the greedy algorithm to maximize its influence.

[1]  Yu Wang,et al.  Community-based greedy algorithm for mining top-K influential nodes in mobile social networks , 2010, KDD.

[2]  Laks V. S. Lakshmanan,et al.  Approximation Analysis of Influence Spread in Social Networks , 2010, ArXiv.

[3]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[4]  Tanya Y. Berger-Wolf,et al.  Finding Spread Blockers in Dynamic Networks , 2008, SNAKDD.

[5]  Shishir Bharathi,et al.  Competitive Influence Maximization in Social Networks , 2007, WINE.

[6]  Vasudeva Varma,et al.  Modelling Action Cascades in Social Networks , 2011, ICWSM.

[7]  John Scott.  What is social network analysis , 2010 .

[8]  M. Nowak,et al.  Evolutionary dynamics in structured populations , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[9]  Laks V. S. Lakshmanan,et al.  Maximizing product adoption in social networks , 2012, WSDM '12.

[10]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Wei Chen,et al.  Efficient influence maximization in social networks , 2009, KDD.

[12]  Aristides Gionis,et al.  Sparsification of influence networks , 2011, KDD.

[13]  Sourav S. Bhowmick,et al.  CASINO: towards conformity-aware social influence analysis in online social networks , 2011, CIKM '11.

[14]  Stefan M. Wild,et al.  Maximizing influence in a competitive social network: a follower's perspective , 2007, ICEC.

[15]  Madhav V. Marathe,et al.  Adversarial models in evolutionary game dynamics , 2001, SODA '01.

[16]  Gao Cong,et al.  Simulated Annealing Based Influence Maximization in Social Networks , 2011, AAAI.

[17]  Matthew Richardson,et al.  Mining the network value of customers , 2001, KDD '01.