Human-AI collaboration requires AI agents to understand human behavior for effective coordination. While advances in foundation models show promising capabilities in understanding and showing human-like behavior, their application in embodied collaborative settings needs further investigation. This work examines whether embodied foundation model agents exhibit emergent collaborative behaviors indicating underlying mental models of their collaborators, which is an important aspect of effective coordination. This paper develops a 2D collaborative game environment where large language model agents and humans complete color-matching tasks requiring coordination. We define five collaborative behaviors as indicators of emergent mental model representation: perspective-taking, collaborator-aware planning, introspection, theory of mind, and clarification. An automated behavior detection system using LLM-based judges identifies these behaviors, achieving fair to substantial agreement with human annotations. Results from the automated behavior detection system show that foundation models consistently exhibit emergent collaborative behaviors without being explicitly trained to do so. These behaviors occur at varying frequencies during collaboration stages, with distinct patterns across different LLMs. A user study was also conducted to evaluate human satisfaction and perceived collaboration effectiveness, with the results indicating positive collaboration experiences. Participants appreciated the agents' task focus, plan verbalization, and initiative, while suggesting improvements in response times and human-like interactions. This work provides an experimental framework for human-AI collaboration, empirical evidence of collaborative behaviors in embodied LLM agents, a validated behavioral analysis methodology, and an assessment of collaboration effectiveness.

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