Social Laws for Multi-agent Coordination in Stochastic Environments

AI agents are increasingly deployed in shared environments where they pursue diverse goals and compete for rewards. This multi-agent competition can lead to behaviors that serve individual gains at collective cost -- for instance, marketing agents may post misleading content as a result of competing for engagement on social media. Human societies address such problems through norms that constrain acceptable behavior, supported by enforcement mechanisms that detect and penalize violations. Motivated by this, we study norm enforcement mechanisms for language model agents. We find that simple enforcement mechanisms are exploited by misaligned agents for competitive advantage, even when they are not explicitly trained or prompted to do so. We thus turn our attention to designing more robust mechanisms, and identify two key ingredients: estimating each agent's reliability over time, and updating this estimate with escalating penalties for repeated misbehavior. Across three simulated environments and a variety of agent populations, mechanisms built on these principles resist exploitation, while still penalizing norm violations at comparable or lower cost than baselines. Our results position norm enforcement mechanisms as scalable levers for shaping agents' behavior, but only when designed to anticipate becoming part of the system they govern. Our code and data are available at https://yaowenye.com/norm-enforcement.

Embodied agents operating in decentralized and partially observable environments have attracted growing attention in recent years. However, existing large language model (LLM)-based agents often exhibit behaviors that are misaligned with their partners or inconsistent with the environment state, leading to inefficient cooperation and poor task success. To address this challenge, we propose a novel framework, Learning Laws of Cooperation (LLawCo), that enables embodied agents to autonomously align with both their partners and task objectives. Our framework allows agents to reflect on past failures to extract misaligned behavioral patterns, which are used to derive high-level behavioral laws, such as "Talk when necessary" and "Wait for partner." These laws are explicitly incorporated into the agents' chains of thought via supervised fine-tuning, aligning their reasoning with task requirements and the behavior of other agents. To evaluate our approach, we introduce PARTNR-Dialog, a large-scale multi-agent communicative and cooperative planning benchmark built on the PARTNR environment. Experiments on existing tasks and our new benchmark demonstrate significant improvements in cooperative efficiency and task success rates. Across four backbone LLMs, our method achieves average success rate improvements of 4.5% on the PARTNR-Dialog benchmark and 6.8% on the TDW-MAT benchmark over state-of-the-art open-source communicative agent frameworks. See the LLawCo project page for details: https://www.merl.com/research/highlights/LLawCo

We propose and study distributionally robust Markov games (DR-MGs) with the average-reward criterion as a crucial framework for multi-agent decision-making under model mismatches and over extended horizons. Under a standard irreducible assumption, we first derive a correspondence between the optimal policies and the solutions of the robust Bellman equation, based on which we further show the existence of a stationary Nash Equilibrium (NE) of the game. We further study DR-MGs under a more general weakly communicating setting. We construct a set-valued map based on the constant-gain optimal robust Bellman operator and show that its value is a subset of the best-response policies. We further prove that this map admits a fixed point, which implies the existence of NE. We then design two algorithms, Robust Nash-Iteration and robust TD Descent, with provably convergent guarantees. Finally, we show that the NE under average-reward can be approximated by the ones for the discounted DR-MGs as the discount factor approaches one. Our studies provide a comprehensive theoretical and algorithmic foundation for decision-making in complex, uncertain, and long-running multi-player environments.