What Could Go Wrong

Pricing algorithms learn to hold prices high, so far only in simulation

Two Q-learning agents reached about 85% of the way to monopoly pricing with no instruction to coordinate, and the economists who reopened their code doubt it would survive a real market.

9 min read2026-09-03

Why this matters

More than a third of the top sellers in one large sample of Amazon items were setting their prices with software as far back as 2015. The question competition lawyers have asked ever since is plain. If two rival programs are each just told to make as much money as they can, could they learn, with no deal and no shared tool, to keep prices high the way a cartel does? This lesson follows that question from the economists who first posed it to the one lawsuit everyone cites. Follow it and you can tell a result proven in a lab from a fear about real markets, and see why the RealPage case, real as it is, belongs in a different box.

Background optional reading

01: Racing dynamics: another argument from this desk, where the thing that goes wrong is competition between the developers, not between their prices.
02: Algorithmic monoculture: what happens when many firms lean on the same model, the near cousin of the shared-tool case here.

A fourth scenario, where nobody agrees to anything

Two competition-law scholars, Ariel Ezrachi and Maurice Stucke, set out four ways pricing algorithms could push prices above the competitive level. Three of them still run on people. A human cartel can use software to carry out a deal it already struck. Rivals can all plug into one supplier's pricing tool and move together through it. Or each firm can adopt an algorithm on its own, hoping the others read the signal and hold their prices up too. The fourth is the one that unsettles them: no person agrees to anything, no firm shares a tool, and independent programs, each told only to maximize its own profit, learn by themselves to keep prices high.¹

What makes the fourth scenario a legal problem is a gap in the law. The behavior it describes is tacit collusion: rivals arriving at high prices with no agreement, just by watching each other and matching. Antitrust law reaches an agreement, a meeting of the minds. It does not reach a high price that no one agreed to. Ezrachi and Stucke's argument is that if machines produce that outcome on their own, it slips past Section 1 of the Sherman Act and its European counterpart, because there is no agreement left to find. In their words, algorithms "may arrive at this anticompetitive outcome on their own."¹

The setting is not hypothetical. By 2015, as Calvano and colleagues note, more than a third of vendors across a sample of over 1,600 best-selling items on Amazon already set prices with software.² The open question is whether those algorithms, left to compete, can teach themselves to collude.

What two Q-learning agents did in a simulated duopoly

The sharpest evidence for the fourth scenario comes from a 2020 study by Emilio Calvano and three co-authors. They built two agents that learn by Q-learning, a plain form of trial and error: the program tries a price, records the reward it brings, and drifts toward the choices that have paid best. They set the two loose in a repeated Bertrand duopoly, a market of two sellers where each period both post a price and the cheaper one wins more of the demand. Each agent saw only past prices, never communicated with the other, and was never told to cooperate. They "consistently learn to charge supra-competitive prices, without communicating," the authors report.²

How high is the question that matters, and the authors put every run on one scale to answer it. Zero is the Bertrand-Nash price, the low level rivals grind each other down to. One is the monopoly price a single owner would set.

\Delta \;=\; \frac{\htmlClass{nb-mc1}{\pi}\;-\;\htmlClass{nb-mc2}{\pi_{N}}}{\htmlClass{nb-mc3}{\pi_{M}}\;-\;\htmlClass{nb-mc2}{\pi_{N}}}

\pithe profit the two algorithms actually earn.
\pi_{N}the competitive Bertrand-Nash profit, where the gain reads 0.
\pi_{M}the monopoly profit one owner would take, where the gain reads 1.

The average profit gain, scaled from competitive at 0 to monopoly at 1.²

Across the whole grid of learning speeds and exploration rates the agents landed between about 70% and 90% of the way to monopoly, roughly 85% at the middle of the grid.² An earlier Q-learning experiment by Klein, which the same authors summarize, had reached only about halfway. Giving the agents a wider set of prices to choose from pushed the gain higher.³

The reason this counts as collusion and not just high prices is what the agents did when one of them cheated. A cut to grab sales was met by the other with a brief price war, and after a few periods both climbed back up. The deviation, the authors write, "gets punished," and the punishment "is only temporary."² That reward-and-punishment reflex is how a cartel holds itself together, and here neither agent was built with it. Both learned it.

Language models push prices up too, and a phrase can swing them

Q-learning is an old method. In 2024 Sara Fish, Yannai Gonczarowski, and Ran Shorrer ran the experiment again with pricing agents built on large language models, the kind of system behind a chat assistant, steered by instructions written in ordinary English. In a similar repeated duopoly, with every channel between the agents shut except the prices they posted, these too reached supra-competitive prices quickly and without being told to.⁴

Their finding turns on a detail that cuts two ways. The pricing moved sharply with the wording of the instruction. A prompt that stressed long-run profit produced far higher prices, sometimes near monopoly, than one that mentioned undercutting and units sold. The authors traced part of the gap to the model working to avoid price wars.⁴ One way to read that deepens the worry: a phrase nobody would flag as an order to collude can tip the pricing toward monopoly. The other way undercuts it: behavior that swings on a single word is fragile, an artifact of what someone typed rather than a strategy the system will hold.

The pattern is not confined to a single good, either. Ryan Lin and three co-authors gave current language models a market of several commodities and watched the agents divide it, each coming to "monopolize specific commodities" by adjusting its quantities and allocation, again with no instruction and no direct messaging between them.⁵ These remain simulations, run in markets the researchers designed and controlled.

Inside the code, the cartel needs a lab

The strongest reply comes from inside the same program. Arnoud den Boer, Janusz Meylahn, and Maarten Pieter Schinkel reran the Calvano algorithm and read closely what it was doing. Their assessment: "there is no immediate reason for alarm."⁶

What holds up

The agents reach high prices across the whole grid of settings, not at one tuned point.²
They hold the price up with a punishment: a cut is met by a short price war, then a return.²
The result survives an outside demand shock, the profit gain falling to about 56% rather than to zero.²

What to be careful about

Every result is a simulation of a stripped-down market.⁶
Convergence takes hundreds of thousands of rounds, about 850,000 at the mid-grid, a patience no firm's profit turns on.⁶
It needs both firms running the same algorithm, at the same settings, started at the same moment.⁶
Against a simpler learning rule, the Q-learning agent earns less, so a profit-seeker would not choose it.⁶

The learning is real and the high price is real. What den Boer and his co-authors show is that every condition holding the price up points away from an open market. It needs the identical program on both sides, the identical settings, the shared starting gun, and a wait far longer than any quarter a business plans for. A review by Florian Dorner reaches the same place from the literature rather than the code. The studies showing learned collusion, he argues, use simple markets and simple algorithms that skip the hard parts of learning in the world, and "it is likely too early to adapt antitrust law to be able to deal with self-learning algorithms colluding in real markets."⁷

The one real case is not the one the worry predicts

There is a single enforcement action people reach for as proof, and it repays reading closely. In August 2024 the Department of Justice and several states sued RealPage. Competing landlords had fed the company's software their own nonpublic data, including rents, renewals, and lease terms. The software used that pooled rival information to recommend rents, with a setting that could apply the recommendation automatically. The complaint pleads the arrangement under Sections 1 and 2 of the Sherman Act, and a November 2025 settlement bars the sharing of that competitively sensitive data.⁸

That is the second scenario, not the fourth. The landlords coordinated through one common tool and their own shared data. Nothing in the case shows independent programs teaching themselves to collude. It shows people using a shared instrument to do the coordinating for them. The OECD, surveying the field in 2023, holds exactly this line between a shared-tool arrangement and autonomous collusion, and records that "as far as the Secretariat is aware, there have not been any autonomous tacit collusion cases."⁹

Three kinds of evidence, and how far each sits from a case of algorithms colluding on their own in a real market.⁹
Register	What has been shown	What it has not shown
Simulation	Q-learning and language-model agents learn supra-competitive prices, 70–90% of the way to monopoly, and punish price cuts.²⁴	That independent firms do this in any real market.
RealPage	Competing landlords fed one shared tool their private data; the DOJ pleads it as an agreement under the Sherman Act.⁸	Any autonomous learning; the coordinating ran through people and a common tool.
Open markets	Nothing yet; the OECD records no autonomous tacit-collusion case.⁹	Whether the simulated result transfers at all.

A further idea sometimes attached to this worry is that pricing agents might learn to coordinate against the people meant to oversee them. Nothing in any of this work stands behind it: these studies are about profit in a market, not about slipping a regulator. It is speculation past the evidence, and worth naming as such. For now the fourth scenario is an argument and a stack of simulations, and the one lawsuit everyone cites is about the second.

The takeaway

The worry is honestly stated and, in a lab, honestly demonstrated. Pricing programs left to compete have learned, on their own, to hold prices most of the way up to monopoly, and to punish each other for cutting, which is what makes it look like collusion rather than coincidence. What has not been shown is any of this happening between real firms in a real market. Every demonstration is a simulation, the learning takes a patience no business has, and it leans on both sides running the identical program from the same start. That is why the researchers who reopened the code see no cause for alarm yet. The one lawsuit that gets cited, against RealPage, is the older kind of coordination: rivals feeding one shared tool their private data, not independent programs teaching themselves. Worth watching, then, and not worth panicking over. The thing to watch for is the first case where neither of those human handholds is present.

Go deeper optional reading

01: Algorithmic Collusion: A Real Problem for Competition Policy?: the four authors' own short account of what they showed and why it is hard to police.
02: Artificial Collusion: the reexamination of the code that argues the danger has been overstated, and sets out what a real threat would take.

A fourth scenario, where nobody agrees to anything

What two Q-learning agents did in a simulated duopoly

Language models push prices up too, and a phrase can swing them

Inside the code, the cartel needs a lab

The one real case is not the one the worry predicts

Sources