Large language model (LLM) agents are increasingly used to negotiate on behalf of individuals and organizations, yet they remain vulnerable to manipulation in repeated multi‑party interactions. Classical multi‑agent systems address this problem with explicit trust and reputation models, whereas most LLM negotiation work treats trust as an emergent property.\ \ We introduce a repeated multi‑party, multi‑issue negotiation framework: a set of recurring agents participates in a sequence of negotiation games, while one participant covertly tries to block agreement. After each game the agents evaluate their counterparts and keep pairwise trust estimates that carry over to future rounds. We compare trust‑aware agents with trust‑agnostic ones and examine how explicit trust influences negotiation outcomes.\ \ Our results reveal a "trust‑agreement gap": trust‑aware agents can identify the adversary within a few games, but accurate trust estimates do not consistently lead to better agreements. Trust improves agreement rates by up to 23 percentage points, but only when agents are explicitly instructed to incorporate it into their decisions. Thus, explicit trust can enhance repeated LLM negotiations, yet its benefit depends critically on how trust is assessed and integrated into the agents' reasoning.\ \ Review