In tacit coordination games with multiple outcomes, purely rational solution concepts, such as Nash equilibria, provide no guidance for which equilibrium to choose. Shelling's theory explains how, in these settings, humans coordinate by relying on focal points: solutions or outcomes that naturally arise because they stand out in some way as salient or prominent to all players. This work studies Large Language Models (LLMs) as players in tacit coordination games, and addresses how, when, and why focal points emerge. We compare and quantify the coordination capabilities of LLMs in cooperative and competitive games for which human experiments are available. We also introduce several learning-free strategies to improve the coordination of LLMs, with themselves and with humans. On a selection of heterogeneous open-source models, including Llama, Qwen, and GPT-oss, we discover that LLMs have a remarkable capability to coordinate and often outperform humans, yet fail on common-sense coordination that involves numbers or nuanced cultural archetypes. This paper constitutes the first large-scale assessment of LLMs' tacit coordination within the theoretical and psychological framework of focal points.

翻译：在具有多重结果的默契协调博弈中，诸如纳什均衡等纯理性解概念无法为均衡选择提供指导。谢林的理论解释了在此类情境下，人类如何通过依赖聚点——即因某种方式对所有参与者而言显得突出或显著而自然浮现的解决方案或结果——来实现协调。本研究将大语言模型（LLMs）作为默契协调博弈的参与者，探讨聚点如何、何时以及为何产生。我们在已有人类实验数据的合作性与竞争性博弈中，比较并量化了大语言模型的协调能力。我们还提出了几种无需学习的方法策略，以提升大语言模型之间及其与人类之间的协调效果。在一系列异构开源模型（包括 Llama、Qwen 和 GPT-oss）上的实验表明，大语言模型展现出卓越的协调能力，且往往优于人类，但在涉及数字或微妙文化原型的常识性协调任务中仍存在不足。本文首次在聚点的理论与心理学框架下，对大语言模型的默契协调能力进行了大规模评估。