  The emergent reasoning and Theory of Mind (ToM) abilities demonstrated by
Large Language Models (LLMs) make them promising candidates for developing
coordination agents. In this study, we introduce a new LLM-Coordination
Benchmark aimed at a detailed analysis of LLMs within the context of Pure
Coordination Games, where participating agents need to cooperate for the most
gain. This benchmark evaluates LLMs through two distinct tasks: (1)
\emph{Agentic Coordination}, where LLMs act as proactive participants for
cooperation in 4 pure coordination games; (2) \emph{Coordination Question
Answering (QA)}, where LLMs are prompted to answer 198 multiple-choice
questions from the 4 games for evaluation of three key reasoning abilities:
Environment Comprehension, ToM Reasoning, and Joint Planning. Furthermore, to
enable LLMs for multi-agent coordination, we introduce a Cognitive Architecture
for Coordination (CAC) framework that can easily integrate different LLMs as
plug-and-play modules for pure coordination games. Our findings indicate that
LLM agents equipped with GPT-4-turbo achieve comparable performance to
state-of-the-art reinforcement learning methods in games that require
commonsense actions based on the environment. Besides, zero-shot coordination
experiments reveal that, unlike RL methods, LLM agents are robust to new unseen
partners. However, results on Coordination QA show a large room for improvement
in the Theory of Mind reasoning and joint planning abilities of LLMs. The
analysis also sheds light on how the ability of LLMs to understand their
environment and their partner's beliefs and intentions plays a part in their
ability to plan for coordination. Our code is available at
\url{https://github.com/eric-ai-lab/llm_coordination}.
