Large language models are reshaping how we model and govern networked socio-technical systems. This dissertation asks: (1) How do different LLM architectures reason about strategic interactions? (2) Can strategic competence be transferred from large to smaller models for scalable simulation? (3) How can we govern multi-agent LLM systems when topology and payoffs are fixed? (4) Can simple communication protocols stabilize small LLM agents in repeated interactions? For (1), systematic game-theoretic evaluations reveal architecture-dependent tradeoffs: some models prioritize payoff structure while others are more context-sensitive. For (2), a fine-tuning pipeline transfers strategic reasoning from a 70B model to a 7B model, preserving decision patterns and enabling large-scale simulations. For (3), framing governance as adaptive information modulation and training an RL manager improves cooperation without changing network structure. For (4), brief pre-play communication reduces behavioral variance in small models and smooths cooperation trajectories. Together, these projects deliver practical tools for using LLMs as realistic agents and for steering collective behavior in deployed multi-agent systems.