When LLM Agents Negotiate: Private Information and Dynamic Bargaining in Supply Chains

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.

Strategic Bargaining in Multi-Buyer Markets: Reinforcement Learning from Verifiable Rewards for LLM Negotiations

Negotiation is a fundamental strategic interaction in management science, characterized by agents attempting to reach agreements while protecting private information, such as reservation costs and hidden valuations. A prevalent yet complex scenario involves a single seller negotiating concurrently with multiple buyers, each possessing heterogeneous, private budgets. In such settings, constrained by a limited number of communication turns, the seller must balance exploring the broader market to discover the highest valuation with concentrating sufficient turns on a single target buyer to secure the best possible outcome. Our analysis reveals a significant gap in standard Large Language Models (LLMs): while these models are linguistically proficient, they fail to act as effective economic decision-makers. Specifically, they exhibit a failure to explore the buyer pool, often fixating on the current highest bid rather than strategically investigating the market to discover latent high valuations. In this paper, we propose a specialized training recipe using Reinforcement Learning from Verifiable Rewards (RLVR). By anchoring the reward function to objective economic outcomes, the strategic balance between market discovery and surplus extraction emerges natively through the learning process. Our results demonstrate that the trained seller undergoes a multi-stage strategic evolution, learning to leverage price anchoring and strategic probing to identify more profitable counterparties. The agent extracts a substantially higher surplus than frontier models by both improving its persuasive bargaining skills and consistently closing deals with high-value buyers. Finally, we show that our seller strategies generalize robustly to unseen buyer negotiation styles and budget distributions.