Controlling a Social Network of Individuals with Coevolving Actions and Opinions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914546752421888 |
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| author | Raineri, Roberta Ye, Mengbin Zino, Lorenzo |
| author_facet | Raineri, Roberta Ye, Mengbin Zino, Lorenzo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06913 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Controlling a Social Network of Individuals with Coevolving Actions and Opinions Raineri, Roberta Ye, Mengbin Zino, Lorenzo Systems and Control Dynamical Systems 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. |
| title | Controlling a Social Network of Individuals with Coevolving Actions and Opinions |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2504.06913 |