Bounded concession for buyer and seller agents
Abstract
Shopping agents are starting to make offers, and store agents are starting to answer them. We describe haggle, a small negotiation engine in which each agent holds a private limit, scores multi-issue offers with its own weights, gives ground on a schedule, and asks its person before crossing an approval line. Messages are restricted to offers and six notes, and every transcript is hash-chained. On seeded scenarios, two agents that give ground early close nearly every possible deal; two that hold out close about half, but keep more of the price range when they do.
1Why this, why now
Retail analysts now describe a near future in which a shopper's agent makes an offer and a retailer's agent counters it, with the shelf price becoming an opening position rather than a fixed number1. The same coverage cites a Mastercard forecast of more than 300 million people routinely shopping through agents by 2030, and reports from supplier negotiations run by software that close most deals without a person in the loop1. Payment companies are opening checkout to any agent2. What is missing is a plain, inspectable piece in the middle: what each agent may offer, when it must stop, and a record both sides can check afterwards.
2Offers and how each side scores them
An offer is a bundle of issues, here price p, delivery days d, warranty months w and an extras level e. Each agent maps every issue to a 0–1 score in its own direction and adds them with its own weights:
U(o) = Σi wi · si(oi), Σi wi = 1
An offer outside an agent's limit, or failing one of its requirements, is never made and never accepted, whatever its score. Because the two sides weigh issues differently, there is usually room to trade: a buyer who cares about warranty and a seller to whom warranty costs little can both gain from a longer one.
3Giving ground
Each agent aims for a target score that falls from its best possible offer toward its worst acceptable one as its rounds run out3. With time t ∈ [0, 1] and floor f:
target(t) = f + (1 − f) · (1 − t1/e)
A large e concedes early ("eager"), e = 1 concedes steadily, and a small e holds out until the end (the "Boulware" style3). The mirror strategy instead gives back the ground it just received, never more slowly than a holdout.
4Choosing the next offer
Many bundles reach the same target. Among those within 0.04 of it, the agent picks the one its model says the other side likes most. The model assumes the other side wants the opposite of us on every issue, and that it cares more about the issues it changes least4. A small penalty keeps each offer close to the other side's last one, so offers converge instead of jumping around.
5Results
Table 1 summarises the benchmark above for four pairings, computed in your browser from seed 7 with 60 scenarios. Deal rate counts only scenarios where the two limits overlap. Buyer's share is the part of that overlap the buyer kept, measured on price alone.
| Buyer vs seller | Deal rate | Buyer's share | Rounds | On the frontier |
|---|---|---|---|---|
| Computing… | ||||
Holdouts close fewer deals but keep more when they do. Eager pairs close almost everything, quickly, yet land on the efficient frontier less often: they agree before the trading on side issues is done. Mirror pairs reach the frontier often but leave the buyer with a small share, because a seller that gives away issues it barely values receives real concessions in return.
6Limits
- Scores are linear per issue; real preferences have thresholds. Requirements cover the hard ones.
- The opponent model is simple, and an opponent can read your concessions just as easily.
- haggle decides what to offer; it doesn't move money. Settlement belongs to the payment layer and to the people involved.
References
- M. Dabo, "The price tag is changing: AI could bring haggling back to retail," Retail Insight Network, via Yahoo Finance, 17 Sep 2026. Link
- "Rezolve Ai opens retail to any AI shopping agent with RezolvePay," GlobeNewswire, 9 Oct 2026. Link
- P. Faratin, C. Sierra and N. R. Jennings, "Negotiation decision functions for autonomous agents," Robotics and Autonomous Systems 24 (1998).
- T. Baarslag, M. Hendrikx, K. Hindriks and C. Jonker, "Learning about the opponent in automated bilateral negotiation," Autonomous Agents and Multi-Agent Systems 30 (2016).