Large language models are increasingly deployed in multi-agent systems for strategic tasks, yet how design choices such as role-based personas and payoff visibility affect behavior remains poorly understood. We investigate whether LLM agents function as payoff-sensitive strategic actors or as identity-driven role followers. Using a 2x2 factorial experiment (persona presence x payoff visibility) with four models (Qwen-7B/32B, Llama-8B, Mistral-7B), we test 53 environmental policy scenarios in four-agent strategic games. We find that personas suppress payoff-aligned behavior: with personas present, all models achieve near-zero Nash equilibrium in Tragedy-dominant scenarios despite complete payoff information. Nearly every equilibrium reached is Green Transition. Removing personas and providing explicit payoffs are both near-necessary for payoff-aligned behavior, enabling only Qwen models to reach 65--90\% equilibrium rates. Our results reveal three behavioral profiles: Qwen adapts to framing, Mistral is disrupted without finding Tragedy equilibrium, and Llama remains near-invariant. We show that the same binary design choice can shift equilibrium attainment by up to 90 percentage points, establishing that representational choices are not implementation details but governance decisions.

翻译：大型语言模型日益被部署在多智能体系统中执行战略性任务，然而角色设定等人格特征和收益可见性等设计选择如何影响行为仍知之甚少。我们探究了LLM智能体究竟是作为对收益敏感的策略行动者，还是作为受身份驱动的角色跟随者。通过采用2×2因子实验设计（人格特征存在与否 × 收益可见性），使用四种模型（Qwen-7B/32B、Llama-8B、Mistral-7B），我们在四智能体战略博弈中测试了53种环境政策情景。研究发现，人格特征会抑制与收益对齐的行为：当存在人格特征时，尽管拥有完整的收益信息，所有模型在"悲剧主导"情景下均达到接近零的纳什均衡。几乎所有达到的均衡都是"绿色转型"。移除人格特征并提供明确的收益对于实现与收益对齐的行为几乎必不可少，仅能使Qwen模型达到65%-90%的均衡达成率。我们的结果揭示了三种行为特征：Qwen能够适应框架设定，Mistral被扰乱但未达到悲剧均衡，而Llama几乎保持不变。我们表明，相同的二元设计选择可使均衡达成率变化高达90个百分点，从而证实表征选择并非实现细节，而是治理决策。