Influence Maximization in Switching-Selection Threshold Models

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.