This May 2026 arXiv preprint (not yet peer-reviewed) models the 2019-2026 U.S. interest in Greenland through multi-agent LLM gameplay, running 3,604 completed simulations across eight frontier models and recording 108,120 actions. The authors recover utility parameters via inverse game theory, showing coercion framing doubles escalation rates from 10.7% to 28.6%. Chinese-origin models weight power differently than Western ones when assigned the U.S. role, while only DeepSeek V3.2 consistently reaches stable acquisition via a five-round metropole strategy. The study is limited by its reliance on synthetic role-play rather than actual diplomatic records and by English-only confirmatory prompts that may understate cultural variance. Beyond the paper, real 2019 Trump administration discussions and Denmark's firm rejection illustrate how human norm enforcement already constrained escalation; the simulations miss how domestic politics and Indigenous Greenlandic self-determination claims could further narrow viable outcomes. Cross-referencing with NATO assurance literature shows the tipping-point game aligns with collective-action thresholds observed in past Article 5 debates. A second lens from AI alignment research indicates that embedding jus cogens language functions like constitutional constraints tested in other multi-agent benchmarks, reducing escalation near baseline. The work positions LLMs as diagnostic tools for alliance stress rather than predictors, highlighting that peaceful U.S. purchase remains statistically marginal at 1.9%.