Negotiation requires more than inferring what the other side wants: it requires using that information to make advantageous offers and counteroffers over multiple turns. We study whether large language model (LLM) agents do this in a controlled multi-attribute bargaining environment. We find that current LLM agents can model a counterparty's preferences, but do not reliably turn that knowledge into strategic bargaining. When given negotiating partner preference information, agents model it accurately and early in their reasoning traces, yet this does not reliably improve outcomes for the informed side. Turn-level analyses show why: agents often respond to what they believe the counterparty values, but do not consistently pair those moves with gains on their own high-value attributes. Sellers are more accommodating overall, and in asymmetric-information conditions, the informed side often makes the more weakly compensated concessions. Because agents fail to leverage this underlying utility structure for strategic advantage, their final agreements are heavily dictated by surface-level opening anchors rather than actual utility weights. Finally, requiring agents to explicitly state concession-for-reciprocity trades before making an offer makes individual turns look more strategic, but ultimately fails to improve the efficiency of the final agreements.