While Large Language Models (LLMs) have been extensively tested in dyadic game-theoretic scenarios, their collective behavior within complex network games remains surprisingly unexplored. To bridge this gap, we present NetworkGames, a framework connecting Generative Agents and Geometric Deep Learning. By formalizing social simulation as a message-passing process governed by LLM policies, we investigate how node heterogeneity (MBTI personalities) and network topology co-determine collective welfare. We instantiate a population of LLM agents, each endowed with a distinct personality from the MBTI taxonomy, and situate them in various network structures (e.g., small-world and scale-free). Through extensive simulations of the Iterated Prisoner's Dilemma, we first establish a baseline dyadic interaction matrix, revealing nuanced cooperative preferences between all 16 personality pairs. We then demonstrate that macro-level cooperative outcomes are not predictable from dyadic interactions alone; they are co-determined by the network's connectivity and the spatial distribution of personalities. For instance, we find that small-world networks are detrimental to cooperation, while strategically placing pro-social personalities in hub positions within scale-free networks can significantly promote cooperative behavior. We validate the robustness of these findings through extensive stress tests across multiple LLM architectures, scaled network sizes, varying random seeds, and comprehensive ablation studies. Our findings offer significant implications for designing healthier online social environments and forecasting collective behavior. We open-source our framework to facilitate research into the social physics of AI societies.

翻译：尽管大语言模型已在二元博弈场景中得到广泛测试，但其在复杂网络博弈中的集体行为仍令人惊讶地未被探索。为填补这一空白，我们提出NetworkGames框架——连接生成式智能体与几何深度学习的系统。通过将社会模拟形式化为由LLM策略驱动的消息传递过程，我们研究了节点异质性（MBTI人格特征）与网络拓扑结构如何共同决定集体福祉。我们实例化了一个由MBTI分类学中不同人格特征的LLM智能体组成的群体，将其置于多种网络结构（如小世界网络与无标度网络）中。通过迭代囚徒困境的大量模拟，我们首先建立基线二元交互矩阵，揭示16种人格配对间微妙的合作偏好，进而证明宏观层面的合作结果无法仅通过二元交互预测，而是由网络连通性与人格空间分布共同决定。例如，我们发现小世界网络不利于合作，而在无标度网络中将亲社会人格策略性地置于枢纽节点则可显著促进合作行为。通过跨多种LLM架构、不同规模网络、随机种子及全面消融实验的压力测试，我们验证了这些发现的稳健性。本研究为设计更健康的在线社会环境及预测集体行为提供了重要启示。我们开源该框架以促进对AI社会物理学的深入研究。