A subjective evidence model for influence maximization in social networks

• We select seeds to maximize influence spread in a social network with competition.
• Influence occurs via subjective evidence exchange in Bayesian hypothesis testing.
• A new formal math model is proposed for parallel cascade influence maximization.
• Lagrangian and iterative seed removal heuristics overcome computational challenges.
• Opponent proximity/strength and campaign timing inform optimal seed locations.

This paper introduces the notion of subjective evidence, which fuels a new parallel cascade influence propagation model. The model sheds light on the phenomena of belief reinforcement and viral spread of innovations, rumors, opinions, etc., in social networks. Network actors are assumed to be testing a Bayesian hypothesis, e.g., for making judgment about the superiority of some product(s) or service(s) over others, or (dis)utility of a given program/policy. The model-based influence maximization solutions inform the strategies for market niche selection and protection, and identification of susceptible groups in political campaigning. The NP-Hard problem of influential seed selection is first solved as a mixed-integer program. Second, an efficient Lagrangian Relaxation heuristic with guaranteed bounds is presented. In small, medium and large-scale computational investigations, we analyze: (1) how the success of an influence cascade triggered in a (sub)community, long exposed to an opposite belief, depends on the structural properties of the underlying social network, (2) to what extent growing (increasing the density of) a consumer network within a market niche helps a company protect the niche, (3) given a competitor׳s strength, when a company should counter the competitor on “their turf”, and when and how it should look for limited-time opportunities to maximally profit before eventually surrendering the market.