Controlling a Social Network of Individuals with Coevolving Actions and Opinions
This work addresses the problem of controlling opinion dynamics in social networks for researchers in network science and control theory, offering a novel framework with theoretical guarantees for a previously unformalized problem.
The paper formulates a control problem for social networks where actions and opinions coevolve, aiming to steer a population from one consensus to another using a committed minority. It derives conditions for success and optimal placement, proving the placement problem is NP-complete and providing efficient algorithms with theoretical guarantees.
In this paper, we consider a population of individuals who have actions and opinions, which coevolve, mutually influencing one another on a complex network structure. In particular, we formulate a control problem for this social network, in which we assume that we can inject into the network a committed minority -- a set of stubborn nodes -- with the objective of steering the population, initially at a consensus, to a different consensus state. Our study focuses on two main objectives: i) determining the conditions under which the committed minority succeeds in its goal, and ii) identifying the optimal placement for such a committed minority. After deriving general monotone convergence result for the controlled dynamics, we leverage these results to build a computationally-efficient algorithm to solve the first problem and an effective heuristics for the second problem, which we prove to be NP-complete. For both algorithms, we establish theoretical guarantees. The proposed methodology is illustrated though academic examples, and demonstrated on a real-world case study.