When Personas Override Payoffs: Role Identity Bias in Multi-Agent LLM Decision-Making

Abstract: LLMs are increasingly deployed in multi-agent systems for strategic tasks, yet how design choices such as role-based personas and payoff visibility affect reasoning remains poorly understood. We investigate whether multi-agent systems function as strategic reasoners capable of payoff optimization or as identity-driven actors that prioritize role alignment over explicit incentives. Using Nash equilibrium achievement as a diagnostic for strategic reasoning, we conduct systematic experiments across four LLM architectures (Qwen-7B, Qwen-32B, Llama-8B, Mistral-7B) in complex environmental decision-making games involving four agents. We show that role identity bias fundamentally alters strategic reasoning even when payoff-optimal equilibria exist and complete payoff information is available. Removing personas and providing explicit payoffs enables Qwen models to achieve high Nash equilibrium rates, indicating that both conditions are necessary for strategic reasoning. In contrast, personas systematically bias equilibrium selection toward socially preferred outcomes: with personas present, all of the achieved equilibria correspond to Green Transition, while models entirely fail to reach equilibrium when Tragedy of the Commons is payoff-optimal. The effect of explicit payoffs depends entirely on persona presence, revealing strong interactions between representational design choices. We also observe clear model-dependent patterns. Qwen architectures are highly sensitive to both personas and payoff visibility, whereas Llama and Mistral exhibit rigid reasoning behavior across conditions. These findings demonstrate that representational choices are substantive governance decisions that determine whether multi-agent systems act as strategic reasoners or identity-driven actors, with important implications for real-world deployment.