Allan Borodin
ABSTRACT
Motivated by applications to word-of-mouth advertising, we consider a game-theoretic scenario in which competing advertisers want to target initial adopters in a social network. Each advertiser wishes to maximize the resulting cascade of influence, modeled by a general network diffusion process. However, competition between products may adversely impact the rate of adoption for any given firm. The resulting framework gives rise to complex preferences that depend on the specifics of the stochastic diffusion model and the network topology.
We study this model from the perspective of a central mechanism, such as a social networking platform, that can optimize seed placement as a service for the advertisers. We ask: given the reported demands of the competing firms, how should a mechanism choose seeds to maximize overall efficiency? Beyond the algorithmic problem, competition raises issues of strategic behaviour: rational agents should not be incentivized to underreport their budget demands.
We show that when there are two players, the social welfare can be 2-approximated by a polynomial-time strategyproof mechanism. Our mechanism is defined recursively, randomizing the order in which advertisers are allocated seeds according to a particular greedy method. For three or more players, we demonstrate that under additional assumptions (satisfied by many existing models of influence spread) there exists a simpler strategyproof (e/e-1)-approximation mechanism; notably, this second mechanism is not necessarily strategyproof when there are only two players.
- K. Apt and E. Markakis. Diffusion in social networks with competing products. In G. Persiano, editor, Algorithmic Game Theory, volume 6982 of Lecture Notes in Computer Science, pages 212--223. Springer Berlin / Heidelberg, 2011. Google Scholar
Digital Library
- S. Bharathi, D. Kempe, and M. Salek. Competitive influence maximization in social networks. In X. Deng and F. Graham, editors, Internet and Network Economics, volume 4858 of Lecture Notes in Computer Science, pages 306--311. Springer Berlin / Heidelberg, 2007. Google ScholarDigital Library
- A. Borodin, M. Braverman, B. Lucier, and J. Oren. Truthful mechanisms for competing submodular processes. CoRR, abs/1202.2097, 2012.Google Scholar
- A. Borodin, Y. Filmus, and J. Oren. Threshold models for competitive influence in social networks. In A. Saberi, editor, Internet and Network Economics, volume 6484 of Lecture Notes in Computer Science, pages 539--550. Springer Berlin / Heidelberg, 2010. Google ScholarDigital Library
- J. J. Brown and P. H. Reingen. Social ties and word of mouth referral behavior. Journal of Consumer Research, 14(3):350--362, 1987.Google ScholarCross Ref
- T. Carnes, C. Nagarajan, S. M. Wild, and A. van Zuylen. Maximizing influence in a competitive social network: a follower's perspective. In Proceedings of the ninth international conference on Electronic commerce, ICEC '07, pages 351--360, New York, NY, USA, 2007. ACM. Google ScholarDigital Library
- D. Centola and M. Macy. Complex contagions and the weakness of long ties. American Journal of Sociology, 113(3):702--734, 2007.Google ScholarCross Ref
- P. Dubey, R. Garg, and B. De Meyer. Competing for customers in a social network: The quasi-linear case. In P. Spirakis, M. Mavronicolas, and S. Kontogiannis, editors, Internet and Network Economics, volume 4286 of Lecture Notes in Computer Science, pages 162--173. Springer Berlin / Heidelberg, 2006. Google ScholarDigital Library
- J. Feldman, M. Henzinger, N. Korula, V. S. Mirrokni, and C. Stein. Online stochastic packing applied to display ad allocation. In Proceedings of the 18th annual European conference on Algorithms: Part I, ESA'10, pages 182--194, Berlin, Heidelberg, 2010. Springer-Verlag. Google ScholarDigital Library
- J. Feldman, A. Mehta, V. Mirrokni, and S. Muthukrishnan. Online stochastic matching: Beating 1-1/e. FOCS, 0:117?126, 2009.Google Scholar
- J. Goldenberg, B. Libai, and E. Mulle. Talk of the network: A complex systems look at the underlying process of word-of-mouth. Marketing Letters, pages 221--223, 2001.Google Scholar
- P. Goundan and A. Schulz. Revisiting the greedy approach to submodular set function maximization. Optimization online, (1984):1--25, 2007.Google Scholar
- S. Goyal and M. Kearns. Competitive contagion in networks. In STOC, pages 759--774, 2012. Google ScholarDigital Library
- M. Granovetter. Threshold models of collective behavior. American Journal of Sociology, (83):1420--1443, 1978.Google Scholar
- D. Kempe, J. Kleinberg, and E. Tardos. Maximizing the spread of influence through a social network. In KDD '03: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, pages 137--146, New York, NY, USA, 2003. ACM. Google ScholarDigital Library
- D. Kempe, J. Kleinberg, and E. Tardos. Influential nodes in a diffusion model for social networks. In L. Caires, G. Italiano, L. Monteiro, C. Palamidessi, and M. Yung, editors, Automata, Languages and Programming, volume 3580 of Lecture Notes in Computer Science, pages 1127--1138. Springer Berlin / Heidelberg, 2005. Google ScholarDigital Library
- J. Kostka, Y. A. Oswald, and R. Wattenhofer. Word of mouth: Rumor dissemination in social networks. In Proceedings of the 15th international colloquium on Structural Information and Communication Complexity, SIROCCO '08, pages 185--196, Berlin, Heidelberg, 2008. Springer-Verlag. Google ScholarDigital Library
- A. Kulik, H. Shachnai, and T. Tamir. Maximizing submodular set functions subject to multiple linear constraints. In Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '09, pages 545--554, Philadelphia, PA, USA, 2009. Society for Industrial and Applied Mathematics. Google ScholarDigital Library
- E. Mossel and S. Roch. Submodularity of influence in social networks: From local to global. SIAM J. Comput., 39(6):2176--2188, 2010. Google ScholarDigital Library
- G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher. An analysis of approximations for maximizing submodular set functions?II. Mathematical Programming, 14(1):265--294, Dec. 1978.Google ScholarDigital Library
- G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher. An analysis of approximations for maximizing submodular set functions?i. Mathematical Programming, 14:265--294, 1978. 10.1007/BF01588971.Google ScholarDigital Library
- R. T. Rockafellar. Convex Analysis (Princeton Landmarks in Mathematics and Physics). Princeton University Press, December 1996.Google Scholar
- T. Schelling. Micromotives and macrobehavior. Norton, 1978.Google Scholar
- Y. Singer. How to win friends and influence people, truthfully: influence maximization mechanisms for social networks. In WSDM, pages 733--742, 2012. Google ScholarDigital Library
- M. Sviridenko. A note on maximizing a submodular set function subject to a knapsack constraint. Operations Research Letters, 32(1):41 -- 43, 2004. Google ScholarDigital Library
Index Terms
- Strategyproof mechanisms for competitive influence in networks
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