We introduce a novel negotiation framework that aims to improve language models' capabilities in non-transparent, non-zero-sum negotiations involving hidden utility functions. Our approach incorporates strategic communication, utility prediction, and self-modeling to more closely simulate real-world negotiation dynamics. By enabling the agent to better understand and adapt to different individuals, this framework helps optimize both individual and group outcomes, overcoming limitations seen in current models. We evaluate our framework by testing different GPT models across different negotiation scenarios, expecting to yield key insights into strategic reasoning, effective communication, and the adaptability of language models in complex interactions.