Do LLMs Beat Nash? Testing Decentralized Coordination in Self-Play Multi-Agent Games

LLM agents are known to deviate from Nash equilibria in strategic interactions, but nobody has looked inside the model to understand why, or asked whether the deviation can be reversed. We do both. Working with four open-source models (Llama-3 and Qwen2.5, 8B to 72B parameters) playing four canonical two-player games, we establish the behavioral picture through self-play and cross-play experiments, then open up the 32-layer Llama-3-8B model and examine what actually happens during a strategic decision. The mechanistic findings are clear. Opponent history is encoded with near-perfect fidelity at the first layer (96% probe accuracy) and consumed progressively, while Nash action encoding is weak throughout, never exceeding 56%. There is no dedicated Nash module. Instead, the model privately favors the Nash action through most of its forward pass, but a prosocial override rooted in pretraining on human text concentrated in the final layers reverses this, reaching 84% probability of cooperation at layer 30. Injecting a learned Nash direction into the residual stream shifts behavior bidirectionally and causally, confirmed through concept clamping. The behavioral experiments surface six scale- and architecture-dependent findings, the most notable being that chain-of-thought reasoning worsens Nash play in small models but achieves near-perfect Nash play above 70B parameters. The cross-play experiments reveal three phenomena invisible in self-play: a small model can unravel any partner's cooperation by defecting early; two large models reinforce each other's cooperative instincts indefinitely; and who moves first determines which Nash equilibrium the system reaches. LLMs do not lack Nash-playing competence. They compute it, then suppress it.

As LLMs become more widely deployed, they are increasingly expected to work alongside other AI agents rather than operating in isolation. Effective coordination in these settings requires agents to communicate, share information and make decisions under uncertainty. We introduce SMAC-Talk, a natural language extension of the StarCraft Multi-Agent Challenge for evaluating LLM-based agents in cooperative multi-agent environments. The environment has several key features such as decentralized control, partial observability and long-horizon decision making. SMAC-Talk includes a natural language communication channel which is used to probe agent coordination and trust. We use this communication channel to construct different evaluation scenarios, including settings with an embedded deceptive communicator that tries to disrupt and deceive allies through communication alone. We provide three agents for benchmarking using 4 models from the Qwen3.5 family and study how reasoning structure, memory and model scale affect coordination between agents. We release SMAC-Talk as an open benchmark to support the research community in developing and evaluating LLM agents in cooperative multi-agent settings.

As language models are increasingly deployed as autonomous agents, they must coordinate with others over long horizons in open-ended interactive tasks. Yet existing evaluations rarely test these demands together, instead emphasising single-agent tasks, short interactions, or highly structured multi-agent settings. We introduce $alem$, a JAX-based benchmark for open-ended multi-agent coordination built on Craftax-like dynamics. Alem embeds procedurally generated coordination tasks, soft specialisation, communication, and controllable coordination difficulty into a long-horizon survival world with exploration, crafting, trading, and combat. We evaluate $13$ modern LLMs zero-shot within homogeneous teams, with trained MARL agents as reference points. Current LLM agents remain far from solving alem, averaging only ~6% normalised return, but their failures are not uniform. On the hardest coordination setting, zero-shot Gemini-3.1-Pro-High approaches MARL agents trained for one billion steps, while GPT-5.4-High achieves strong base-task reward but much lower coordination reward. This contrast shows that individual task competence does not imply coordination competence. Ablations show that communication is the largest contributor to coordination, while memory and reasoning help when used to maintain multi-step plans. Overall, our results identify coordination as a distinct bottleneck for frontier LLM agents, separate from single-agent capabilities. Alem makes this bottleneck measurable and provides a controlled testbed for developing agents that communicate, allocate roles, and execute shared plans. Code is available at https://github.com/alem-world/alem-env.