The Curse of Rationality in Dynamic Public Goods Games: How LLM Agents Navigate Phase Transitions

Large language models (LLMs) are increasingly deployed as interactive agents, motivating the study of their cooperative behavior in social dilemmas through multi-agent game simulations. However, many existing benchmarks emphasize static or per-round payoffs and underrepresent settings where groups must incursunk costs before any returns are available. To explore whether agents can bridge the initial phase of ``zero immediate return,'' this study proposes a Phase-Transition Public Goods Game (Phase-Transition PGG), comparing Qwen2.5-7B (high reasoning capability) with Llama3-8B (high instruction-following/intuition). Through experiments, we surprisingly find that high intelligence does not mean high collaborative capacity. The rationally conceited Qwen veered toward free-riding, leading to systemic stagnation; conversely, Llama successfully entered the profitable stage by relying on fuzzy altruistic intuitions. We further show that communication quality is pivotal: fine-grained, numeric commitments support verification and coordination, substantially increasing the level and stability of cooperation, whereas vague slogan-like messages yield only limited improvements. Finally, we observe that external incentive schemes can be ineffective during resource-scarce construction phases, while heterogeneous populations are more likely to escape deadlock. Together, these results highlight a failure mode for highly rational agents in thresholded social dilemmas and suggest that designing cooperative LLM systems requires more than improving individual reasoning.