Abstract
We consider the problem of modeling competitive diffusion in real world social networks via the notion of ChoiceGAPs which combine choice logic programs and Generalized Annotated Programs. We assume that each vertex in a social network is a player in a multi-player game (with a huge number of players) — the choice part of the ChoiceGAPs describes utilities of players for acting in various ways based on utilities of their neighbors in those and other situations. We define multi-player Nash equilibrium for such programs — but because they require some conditions that are hard to satisfy in the real world, we introduce the new model-theoretic concept of strong equilibrium. We show that strong equilibria can capture all Nash equilibria. We prove a host of complexity (intractability) results for checking existence of strong equilibria and identify a class of ChoiceGAPs for which strong equilibria can be polynomially computed. We perform experiments on a real-world Facebook data set surrounding the 2013 Italian election and show that our algorithms have good predictive accuracy with an Area Under a ROC Curve that, on average, is over 0.76.
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Notes
- 1.
Specifically, [19] shows that ChoiceGAPs can express cascade models such as [8] used to model the spread of “favorites” in Flickr, tipping models such as the Jackson-Yariv model of product adoption in economics [12], the SIR and the SIS models of disease spread [2, 11], as well as homophilic models such as those involving mobile phone usage [4].
- 2.
As in the case of Generalized Annotated Programs [14], note that each annotation function symbol f of arity i denotes some fixed pre-theoretically defined function from \([0,1]^i\) to [0, 1].
- 3.
We refer to \(A_0:f(\mu _1,\dots ,\mu _n)\) as the head of the rule, and to \(A_1:\mu _1,\dots ,A_n:\mu _n\) as the body of the rule.
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Parts of this work were supported by ARO grant W911NF1610342.
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Serra, E., Spezzano, F., Subrahmanian, V.S. (2016). ChoiceGAPs: Competitive Diffusion as a Massive Multi-player Game in Social Networks. In: Schockaert, S., Senellart, P. (eds) Scalable Uncertainty Management. SUM 2016. Lecture Notes in Computer Science(), vol 9858. Springer, Cham. https://doi.org/10.1007/978-3-319-45856-4_21
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