Mutual Recursive Improvement: Toward Co-evolving Multi-Agent Societies in Games

How can LLM agent societies adapt their cooperation as conditions change, and how are the resulting benefits distributed? Strong individual reasoning does not ensure effective coordination among agents with distinct interests, particularly when changing environments make existing strategies and commitments inappropriate. We introduce **Mutual Recursive Improvement (MRI)**, a framework connecting individual learning with institutional adaptation through an interaction–reflection–revision cycle. Human-inspired interventions help agents interpret outcomes, reassess experience, and revise private rules and shared commitments. These revisions shape subsequent interactions, whose outcomes inform further adjustment, while model parameters remain frozen and agents receive no explicit instruction to maximize collective profit. We evaluate eight LLMs over 50 simulated quarters in market-conditioned Dictator, Trust, and Public Goods games, using disclosed historical SPDR S&P 500 ETF Trust (SPY) returns. The final configuration improves allocation quality and collective surplus over baseline in 23 of 24 model–game combinations each, with both improving in 22. Mean allocation quality increases by $29.7$, and mean regime-aligned cooperation rises from $22.0$ to $64.6$. These findings demonstrate the potential of structured interventions to support adaptive cooperation through revisable experience and commitments. The code will be open sourced upon acceptance.