Thirteen LLMs tested on one-shot coordination: frontier models beat Nash, but the advantage vanishes at four or more agents

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'Do LLMs Beat Nash?' (arXiv:2608.12547, Aug 12, 2026, Sinishaw, Zhu, Meriaux, Dudek) tested 13 LLMs in one-shot matrix games across seven strategic archetypes with 2–10 actions per player, where each model knew only that its opponents were running identical software. Frontier hosted models consistently exceeded Nash equilibrium baselines and sometimes approached optimal joint outcomes; most open-weight models showed only modest, structure-dependent gains. The finding that matters for multi-agent builders: two-player coordination ability did not transfer to teams of four or more, where performance declined substantially.