Same Persona, Different Language, Different Deal: Cross-Lingual Effects in LLM Negotiation

Tell an LLM negotiator to be ``headstrong'' and it should hold firm on price, but does that instruction retain the same behavior in every language? To test this, we use identical buyer and seller instances of Gemini 3.6 Flash to negotiate the same 12 CraigslistBargain scenarios in English and Korean. The pilot-scale $2\times2\times3$ design crosses interaction language, seller urgency (none or strong), and buyer persona (cooperative, neutral, or headstrong), yielding 432 attempted negotiations. We call this property \emph{cross-lingual social-policy fidelity}: whether a prompt-defined social policy produces the same behavioral effect regardless of interaction language. It often does not. Korean negotiations reached agreement far more often than English (77.3\% vs.\ 52.5\%, a 24.8-point gap, Holm-adjusted $p=.0039$), but only for neutral and headstrong buyers; cooperative buyers were already near-ceiling in both languages. Buyers' opening offers barely differed by language; the gap instead emerged later, through larger seller concessions and a smaller final gap in Korean, and agreed prices were also lower in Korean. This language effect is not an artifact of a single model: repeating the full negotiation with Qwen3 as both agents reproduces the same direction of effect on both agreement rate ($+13.9$pp Korean vs.\ Gemini's $+24.8$pp) and conditional final price ($-18.8$pp vs.\ $-25.0$pp), smaller in magnitude but consistent in sign. Another model labeled every turn for face-threatening acts and politeness-mitigation strategy: Korean dialogue showed consistently higher mitigation, most sharply for sellers (11.7\% vs.\ 3.6\% of face-threatening turns), and a higher share of positive-politeness strategies. These results show that such a policy can produce different real-world behavior, not just different wording, when only the interaction language changes. This shift holds across at least two different underlying models.