LLM-Driven Social Influence for Cooperative Behavior in Multi-Agent Systems

This paper presents a novel approach to fostering cooperative behavior in multi-agent systems (MAS) through Large Language Model (LLM)-driven social influence. We propose a theoretical framework where agents’ decision-making processes are influenced not through direct action but by subtle, narrative-driven influences disseminated by LLMs. These influences guide agents toward cooperative behaviors, such as rural repopulation, without requiring explicit policy interventions. We introduce a formal model grounded in game theory and social network dynamics, where agents balance the direct benefits of action with the indirect payoffs of LLM-guided influence. Using NASH equilibrium and Evolutionarily Stable Strategies (ESS), we demonstrate how cooperative behaviors emerge even when agents remain inactive but are subtly influenced by LLMs. Our experimental simulations validate the model, showing a strong positive correlation between network centrality and influence propagation ( $r = 0.969,\; p \lt 0.006$ ). Furthermore, temporal analysis reveals that the average influence increases from approximately 0.05–0.06 in the initial steps to 0.08–0.09 in later stages, indicating a cumulative and self-sustaining trend. In addition, the influence values exhibit a near-normal distribution (Shapiro-Wilk test, $p = 0.285$ ) and yield a large effect size (Cohen’s $d = 4.530$ ) when comparing agents with high versus low network centrality. Through visualization techniques and statistical metrics, we demonstrate the effectiveness of the proposed framework and identify promising directions for future research in AI-driven social influence. This study highlights the potential of LLM-driven narratives as a cost-effective, scalable alternative to traditional policy interventions, offering a new paradigm for promoting societal cooperation in areas such as rural repopulation, sustainability, and community development.