The Automated but Risky Game: Modeling and Benchmarking Agent-to-Agent Negotiations and Transactions in Consumer Markets

Shenzhe Zhu, Jiao Sun, Yi Nian, Tobin South, Alex Pentland and Jiaxin Pei study what happens when both sides delegate a purchase to language-model agents. Their benchmark separates obtaining a favorable price from respecting the limits of the delegation: an agent can bargain effectively yet accept a transaction its user did not authorize. This account concerns arXiv v4, dated September 20, 2025.^[1]

How the negotiation works

The researchers compile 100 products across electronics, motor vehicles and real estate, with retail prices and product information collected from public sources. Wholesale costs are estimated by GPT-4o. The main evaluation samples 50 products and uses five buyer budgets for each: 120% of retail price, retail price, the midpoint between retail and cost, cost itself, and 80% of cost. The last condition deliberately leaves no price that satisfies both parties’ constraints.^[1]

Both agents know the retail price and product description. Only the seller receives the estimated cost; only the buyer receives its spending limit. The buyer should obtain a discount without exceeding its budget, while the seller should preserve its margin without selling below cost. These are instructions to the models, rather than externally enforced transaction checks. The buyer opens with an offer, and the agents alternate messages. GPT-4o extracts prices and judges whether the buyer accepts, rejects or continues. An unresolved negotiation ends as a rejection after 30 rounds.^[1]

The main round robin tests nine models as both buyer and seller, including against themselves. Buyer performance is measured through the price reduction from retail. Seller relative profit compares aggregate profit with the lowest-profit seller, GPT-3.5, so a model’s margin and its ability to close deals both matter. A high margin on the few deals completed does not necessarily produce the highest total profit.^[1]

Bargaining performance and constraint failures

In this setup, o3 performs strongly at obtaining discounts and resisting them. GPT-4.1 and DeepSeek-R1 achieve seller total profits about 13.3 and 12 times the GPT-3.5 baseline, respectively. These are ratios within the simulated product and opponent mix, rather than expected returns for actual shoppers. A separate six-size Qwen2.5 comparison finds better bargaining outcomes at larger scales. Correlations with other capability benchmarks use only six representative models and do not isolate intelligence or size as the cause of a negotiation advantage.^[1]

The paper distinguishes four failures:^[1]

• Constraint violations: accepting a price above the buyer’s budget or below the seller’s cost. The reported overall rates for Qwen2.5-7B are 11.76% out of budget and 7.91% below cost; each uses all attempted negotiations as its denominator. Such failures become especially relevant in the deliberately infeasible low-budget condition.
• Overpayment: accepting more than the listed retail price, measured among completed deals. Dialogue examples show buyers revealing generous budgets despite contrary guidance, after which sellers anchor their demands to those budgets. This is a source-reported pattern, not a separately isolated causal test.
• Deadlock: reaching the 30-round limit without agreement or an explicit rejection. Continuing a futile bargain consumes calls even though the final transaction is rejected.
• Early settlement: higher budgets are associated with smaller discounts, as agents accept an affordable offer instead of continuing to bargain. Affordability and obtaining the best price are different objectives.

A limited mitigation result

For the Qwen2.5-7B buyer, the authors search over 96 prompt configurations using an online bandit. Configurations vary negotiation instructions, and rewards penalize overpayment in high-budget settings, budget violations in low-budget settings, and deadlock. This selects a prompt; it does not train the underlying language model’s weights.^[1]

Table 2 reports out-of-budget errors falling from 18.4% to 1.3% in this mitigation experiment. Overpayment changes from 8.1% to 8.3%, while deadlock remains 4.0%. The 18.4% baseline belongs to this experiment, rather than the 11.76% overall round-robin rate above. The result demonstrates a targeted improvement, not a general solution to all three anomalies or a guarantee for other models and markets.^[1]

Why delegated authority matters

The study connects Agentic Inequality with Multi-Agent Risks: different agents can secure different outcomes for their users, while even a completed deal may violate a principal’s limits. Compare The Illusion of Rationality: Tacit Bias and Strategic Dominance in Frontier LLM Negotiation Games for a separate bargaining evaluation. Neither benchmark establishes observed consumer losses.

Model-estimated costs, automated price extraction and judging, selected products, prompts and opponents all shape these measurements. The simulations contain no actual transfer of money or property. Their practical lesson is that bargaining success and permission to transact require separate checks: a favorable discount cannot compensate for crossing a spending limit.^[1]