On the Behavior of LLMs as Mediators in Bilateral Trade

Large Language Model (LLM) agents increasingly act on behalf of people in commerce, including as mediators that help a buyer and a seller reach a deal. Evaluating such mediators is challenging since (i) their pricing policy is latent: we observe the prices they propose, not the rule that produces them, and (ii) outcomes such as deal rates depend on how the counterparties respond, so they cannot separate a good policy from a favorable environment. To address these challenges, we study LLM mediators in multi-round bilateral trade with private valuations, pair them with persona-parameterized deterministic agents whose responses are known by construction, and recover each mediator's revealed policy with a counterfactual audit that patches one input of the negotiation history at a time. Across 504 market configurations and three frontier model families, we find three consistent behaviors: buyer-facing proposals concede toward the buyer while seller-facing proposals stay near compromise prices, later proposals are driven mainly by the mediator's own earlier proposals rather than by the parties' offers, and the mediator filters offers by trajectory, tracking concessions that continue the bargaining path while ignoring offers that reverse it. We show that this filtering removes the gain from retracting a concession but leaves an incentive to stall, and we derive the feasibility horizon, surplus decomposition, and mechanism-design ceilings of the environment.