Manipulating opinion dynamics in social networks in two phases

International audience; We propose a setting for two-phase opinion dynamics in social networks, where the final opinion of a node in the first phase acts as its initial biased opinion in the second phase. In this setting, we study the problem of two camps aiming to maximize adoption of their respective opinions by strategically investing on nodes, where the effectiveness of a camp's investment on a node depends on the node's initial bias. We propose an extension of Friedkin-Johnsen model for our setting, and hence formulate the utility functions of the camps. For the non-competitive case where only one camp invests, we present a polynomial time algorithm for determining an optimal way to split the camp's budget between the two phases. For the case of competing camps, we show the existence of Nash equilibria under reasonable assumptions, and that they can be computed in polynomial time. Our main conclusion is that, if nodes attribute high weightage to their initial biases, it is advantageous to have a high investment in the first phase, so as to exploit the manipulated biases in the second phase.