Parallelism or Concession? Concurrency-Aware Procurement Negotiation for Agentic Commerce

As LLM agents move from decision support to autonomous procurement, firms need to know whether delegated negotiators create value, divide it predictably, and avoid money-losing contracts. We study this in a canonical supply chain bargaining problem: a buyer with private demand information negotiates a quantity-payment contract with an uninformed seller. We benchmark nine LLMs from OpenAI, Google, and Alibaba against a validated Perfect Bayesian Equilibrium across 9,840 LLM-to-LLM negotiations. First, capability governs value creation. Agents agree in 98.9% of negotiations and capture 95.4% of first-best surplus undiscounted, but average 2.98 rounds against the benchmark's 1.25, and this delay erodes 21-34% of surplus. Capability also governs reliability: baseline models accept individually irrational contracts in 19.2% of cases, versus 0.0-0.6% at mid-tier and flagship, making automated profit verification the binding guardrail below that threshold. Second, surplus capture is relational. Provider identity predicts who captures surplus better than capability rank: self-play buyer shares average 40% for OpenAI, 50% for Google, and 70% for Alibaba's Qwen, an ordering that survives restricted communication and no discounting. Reversing which provider sells moves the division by 7-18 percentage points, and the capable Qwen flagship is the weakest cross-family seller: vendor choice is a first-order distributional decision. Third, the prompt is a strategic lever. Delegation separates the principal's economic patience from the agent's prompted strategic patience, a free deployment choice that is the single strongest driver of surplus division (90% of explained variance). Together these establish an equilibrium-referenced audit of AI agents along three dimensions: discounted efficiency, distributional profile, and operational reliability.

Negotiation is a central mechanism of economic exchange, shaping markets, procurement, labor agreements, and resource allocation. It is also a canonical testbed for agentic language models, requiring multi-turn interaction under hidden preferences, strategic communication, and binding constraints. These properties make negotiation hard to evaluate: unlike math or code, it has no intrinsic verifier. Existing LLM negotiation evaluations rely on LLM-vs.-LLM interaction or aggregate outcomes such as deal rate, leaving failures opaque. We introduce Terms-Bench, short for Testbed for Economic Reasoning in Multi-turn Strategy, a Bayesian-game framework that makes the environment itself the verifier by specifying the counterpart's latent type, policy, and payoff structure. We instantiate it in bilateral price negotiation, where the counterpart's private state and simulator policy are hidden from the agent but observable to the evaluator. This turns the counterpart from a black-box opponent into a diagnostic instrument, enabling agent-attributable failure analysis and oracle-reference optimality gaps. Evaluating 13 LLM agents spanning frontier systems from major providers, Terms-Bench turns negotiation evaluation from aggregate ranking into actionable diagnosis: where agents fail, why they fail, and what to strengthen. Empirically, frontier models saturate deal rate yet diverge in surplus extraction, cue use, belief calibration, and compliance, revealing agent-specific bargaining bottlenecks masked by prior benchmarks.

Freight brokerages negotiate thousands of carrier rates daily under dynamic pricing conditions where models frequently revise targets mid-conversation. Classical time-dependent concession frameworks use a fixed shape parameter $β$ that cannot adapt to these updates. Deriving $β$ from the live spread enables adaptation but introduces a new problem: a pricing shift can cause the formula to retract a previous offer, violating monotonicity. LLM-powered brokers offer flexibility but require expensive reasoning models, produce non-deterministic pricing, and remain vulnerable to prompt injection. We propose a two-index anchor-and-resume framework that addresses both limitations. A spread-derived $β$ maps each load's margin structure to the correct concession posture, while the anchor-and-resume mechanism guarantees monotonically non-decreasing offers under arbitrary pricing shifts. All pricing decisions remain in a deterministic formula; the LLM, when used, serves only as a natural-language translation layer. Empirical evaluation across 115,125 negotiations shows that the adaptive $β$ tailors behavior by regime: in narrow spreads, it concedes quickly to prioritize deal closure and load coverage; in medium and wide spreads, it matches or exceeds the best fixed-$β$ baselines in broker savings. Against an unconstrained 20-billion-parameter LLM broker, it achieves similar agreement rates and savings. Against LLM-powered carriers as more realistic stochastic counterparties, it maintains comparable savings and higher agreement rates than against rule-based opponents. By decoupling the LLM from pricing logic, the framework scales horizontally to thousands of concurrent negotiations with negligible inference cost and transparent decision-making.