Preventing Unraveling in Social Networks: The Anchored k-Core Problem
We consider a model of user engagement in social networks, where each player incurs a cost to remain engaged but derives a benefit proportional to the number of engaged neighbors. The natural equilibrium of this model corresponds to the k-core of the social network — the maximal induced subgraph with minimum degree at least k.
We study the problem of “anchoring” a small number of vertices to maximize the size of the corresponding anchored k-core — the maximal induced subgraph in which every non-anchored vertex has degree at least k. This problem corresponds to preventing “unraveling” — a cascade of iterated withdrawals. We provide polynomial-time algorithms for general graphs with k = 2, and for bounded-treewidth graphs with arbitrary k. We prove strong inapproximability results for general graphs and k ≥ 3.
KeywordsSocial Network General Graph Tree Decomposition Full Version Pure Nash Equilibrium
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- 3.Bodlaender, H.L., Koster, A.M.C.A.: Combinatorial optimization on graphs of bounded treewidth. Comput. J., 255–269 (2008)Google Scholar
- 4.Burke, M., Marlow, C., Lento, T.: Feed me: motivating newcomer contribution in social network sites. In: CHI (2009)Google Scholar
- 9.Ellison, N.B., Steinfield, C., Lampe, C.: The Benefits of Facebook Friends: Social Capital and College Students’ Use of Online Social Network Sites. Journal of Computer-Mediated Communication (2007)Google Scholar
- 10.Farzan, R., Dabbish, L.A., Kraut, R.E., Postmes, T.: Increasing commitment to online communities by designing for social presence. In: CSCW (2011)Google Scholar
- 11.Katz, M.L., Shapiro, C.: Network externalities, competition, and compatibility. American Economic Review 75(3), 424–440 (1985)Google Scholar
- 12.Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: KDD, pp. 137–146 (2003)Google Scholar
- 15.Mossel, E., Roch, S.: On the submodularity of influence in social networks. In: STOC, pp. 128–134 (2007)Google Scholar
- 16.Saaskilahti, P.: Monopoly pricing of social goods. Technical report, University Library of Munich, Germany (2007)Google Scholar
- 17.Schelling, T.C.: Micromotives and Macrobehavior. Norton (1978)Google Scholar