Optimal multiphase investment strategies for influencing opinions in a social network

We study the problem of two competing camps aiming to maximize the adoption of their respective opinions, by optimally investing in nodes of a social network in multiple phases. The final opinion of a node in a phase acts as its biased opinion in the following phase. Using an extension of Friedkin-Johnsen model, we formulate the camps' utility functions, which we show to involve what can be interpreted as multiphase Katz centrality. We hence present optimal investment strategies of the camps, and the loss incurred if myopic strategy is employed. Simulations affirm that nodes attributing higher weightage to bias necessitate higher investment in initial phase. The extended version of this paper analyzes a setting where a camp's influence on a node depends on the node's bias; we show existence and polynomial time computability of Nash equilibrium.