Overview
This project develops the mathematical foundations for reasoning about adversarial influence in social networks. The long-term goal is a principled theory of how opinion dynamics play out when multiple external actors compete — one that can explain phenomena like polarization, the diminishing returns of influence spending, and the resilience or vulnerability of particular network structures.
This work is a first step: we establish the problem formally, show it is harder than it looks even under simple dynamics, and demonstrate that tractable approximations can still capture the essential structure of the game.
The Problem Setting
At the core of the model is a social network of individuals whose opinions evolve over time by averaging the views of their neighbors — a process that, left alone, tends to pull communities toward consensus. The question is what happens when that process is disrupted by outside actors.
We model external players — campaigns, outlets, or any entity seeking to shift opinion — as additional nodes in the network who broadcast a fixed viewpoint. Each player has a limited budget that controls how much weight any individual in the network places on their broadcast. The players act simultaneously, and the network’s long-run opinion is determined by all of their choices together.
This setup captures something important: influence is not additive. When multiple players compete for the same individuals, their effects partially cancel — and the network’s response depends on the full configuration of everyone’s strategy, not just your own.
Results
The most immediate result is that the problem is tractable: we can find good strategies efficiently even for large networks, which is a prerequisite for any deeper scientific analysis. Without fast solvers, studying how outcomes vary with network structure, budget size, or number of players would be computationally prohibitive.
With that foundation in place, the experiments begin to reveal the shape of the problem. On small, interpretable networks, the solutions behave as expected — players concentrate influence on well-connected individuals positioned between competing factions, rather than wasting budget on those already aligned or unreachable. This suggests the model is capturing something real about the structure of strategic influence.
The more surprising finding emerges from varying budget sizes across larger networks: competition creates diminishing and eventually negative returns to influence spending. As all players increase their budgets together, they increasingly cancel each other out — the network ends up less perturbed than it would have been under moderate spending. This is a property of the competitive equilibrium, not any individual strategy, and it points toward a richer set of questions about how budget levels, number of players, and network topology interact to determine outcomes.
Contributors
Renukanandan Tumu, Cristian Ioan Vasile, Victor Preciado, Rahul Mangharam
Citation
@misc{tumu2025adversarialsocialinfluence,
title = {Adversarial Social Influence: Modeling Persuasion
in Contested Social Networks},
author = {Renukanandan Tumu and Cristian Ioan Vasile
and Victor Preciado and Rahul Mangharam},
year = {2025},
eprint = {2510.01481},
archivePrefix = {arXiv},
primaryClass = {cs.SI},
url = {https://arxiv.org/abs/2510.01481},
}
