Large language models are increasingly used as interacting agents, but it remains unclear how robust their coordination is when public communication is unreliable. We study this question in iterated $N$-player Stag Hunt games played by homogeneous LLM groups under controlled programmatic action inversion, which changes both the public transcript and the actions used for execution. Across an experimental grid spanning group sizes, coordination thresholds, corruption levels, and seven LLMs, we observe three main patterns. First, honest agents' pre-flip Stag choices decline as corruption increases, but the sharp fall in public success is primarily mechanical. In the focal $N=5,M=3$ setting, pre-flip success remains 78% at 80% corruption, while public success falls to 12%. Second, honest choices are associated with the public history available at decision time, particularly under high corruption. Third, three threshold-style public-report benchmarks yield similar action-match rates to the LLM agents, showing substantial descriptive agreement between LLM decisions and these benchmarks. Overall, our results show that original choices, public actions, and executed outcomes must be separated when evaluating multi-agent robustness, as corrupted communication can severely and predictably degrade mutually beneficial cooperation.

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