Algorithmic collusion: what the pricing experiments found

Algorithmic collusion is pricing software learning to hold prices above the competitive level with no instruction to do so and no agreement between the firms. Fish, Gonczarowski and Shorrer adopt a broad definition from Abada and colleagues: supracompetitive outcomes produced by learning algorithms without human design to produce them. The founding experiment, published in the October 2020 American Economic Review by Emilio Calvano, Giacomo Calzolari, Vincenzo Denicolò and Sergio Pastorello, found that simple Q-learning programs consistently learned to charge supracompetitive prices without communicating, and that they punished price cuts.

High prices are not enough

Calvano and colleagues separate collusion from high prices. Citing Joseph Harrington (2018), they say collusion requires a reward-punishment scheme that gives firms an incentive to keep pricing above the competitive level. Without one, high prices may only mean the programs failed to optimize. The distinction matters, they argue, because programs that grossly fail to optimize would likely be dropped quickly by the firms using them.

The paper measures outcomes with an average profit gain, Delta. Delta is 0 at the profit of the one-shot Bertrand-Nash equilibrium, the competitive benchmark, and 1 at the profit of full collusion, as if one monopolist ran both firms. In the baseline market, the price-cost margin is about 47 percent at the competitive equilibrium and about twice that under perfect collusion.

The 2020 Q-learning experiments

Q-learning is a reinforcement-learning method that estimates, by trial and error, the discounted payoff of each action in each state, with no model of the market. The baseline is a symmetric duopoly with logit demand. Each program picks from 15 prices running from below the competitive price to above the monopoly price, remembers only the last period's prices, and discounts the future at 0.95. Each set of parameters is an experiment of 1,000 sessions. A session counts as converged when neither program's strategy changes for 100,000 consecutive periods. At the midpoint of the parameter grid, that took 850,000 periods on average.

Across the grid, Delta ranged from 70 to 90 percent, with prices almost always above the one-shot equilibrium but rarely at monopoly. In the representative experiment, only 27.7 percent of sessions ended with both programs charging the same constant price. The rest showed asymmetric prices or cycles. Delta fell from 85 percent with two firms to 64 percent with three and 56 percent with four.

Punishment and a gradual return

To test for a reward-punishment scheme, the authors forced one program to cut its price for one period to the short-run best response, then let both run. The cut was punished. In more than 95 percent of cases, the punishment made it unprofitable. After an initial price war, prices returned gradually toward their earlier level, and in most cases the punishment ended after 5 to 7 periods.

The authors never observed grim-trigger strategies, which they note would trap both programs in a protracted punishment phase once either one experimented. The pattern looked more like the stick-and-carrot strategies of Abreu (1986), though milder. With a discount factor of 0.35, Delta dropped to 16 percent, and programs with no memory also earned modest gains. The authors conclude that the programs price near the one-shot equilibrium when it is the only equilibrium. The authors state limits: the model is stylized, extensions were tested one at a time, and learning took so many periods that, at a few minutes per period, it would span several years or more.

Variations and other learning designs

When one firm's cost fell to a quarter of the other's, Delta fell from 0.849 to 0.713. Random demand shocks cut Delta from 85 to 80 percent, or to 70 percent with larger shocks. Random entry and exit by an outside firm hindered collusion most: Delta fell below 60 percent, and equilibrium play appeared in under 10 percent of sessions. A 2021 follow-up with imperfect monitoring found collusion again, given enough learning time, sustained by price wars that adverse demand shocks could also trigger.

Asker, Fershtman and Pakes, in the May 2022 AEA Papers and Proceedings, report that synchronous learning, which estimates what untaken prices would have earned, can lead to competitive pricing, while asynchronous learning can lead to near-monopoly prices. Timo Klein's 2021 study of sequential pricing found collusive equilibria with few prices and supracompetitive asymmetric cycles with more. Abada and Lambin, in a 2023 study of battery operations, argue that seeming collusion could come from imperfect exploration rather than sophistication.

Language-model agents and market data

Fish and colleagues ran GPT-4 pricing agents in the same logit market. A regression on their price paths fits a reward-punishment scheme in which a rival's low price is met with low prices over several periods, with decaying intensity. When the authors reset runs and implanted reasoning text about avoiding price wars, prices came out substantially higher. A February 2026 rerun on GPT-5.2 gave an average price of 1.79, between a monopoly price of 1.92 and a competitive price of 1.47. The authors call the environment simple, with one fixed time horizon.

Market data come from German retail gasoline, where pricing software became widely available in 2017. The 2024 Journal of Political Economy article by Assad, Clark, Ershov and Xu finds that adoption raised margins only for stations that were not monopolists, and in duopoly and triopoly markets only when all stations adopted.

What to check

• Does a claim of collusion show that price cuts were punished, or only that prices were high?
• How long did the agents learn? Q-learning took 850,000 periods on average at the grid midpoint.
• How many competitors were in the market, and could firms enter and exit?
• Did the agents learn synchronously or asynchronously, and how wide was the set of prices?
• Could the agents communicate in any way other than through the prices they set?
• Is the evidence from a simulation or from market data?

Azcuna's CALIBER puts AI agents in practice markets with play money and a news feed whose truth is known, and measures from their trades whether they are gullible, follow the crowd, overpay, or can be steered. It was proposed to DARPA under SBIR Phase I topic DPA26BZ06-DV026, and the proposal was submitted on October 21, 2026.

Sources

1. 1Artificial Intelligence, Algorithmic Pricing, and Collusion · Calvano, Calzolari, Denicolò and Pastorello, American Economic Review 110(10), October 2020 (University of Rome Tor Vergata repository copy)
2. 2Algorithmic collusion with imperfect monitoring · Calvano, Calzolari, Denicolò and Pastorello, International Journal of Industrial Organization 79, 2021 (RePEc record and abstract)
3. 3Artificial Intelligence, Algorithm Design, and Pricing · Asker, Fershtman and Pakes, AEA Papers and Proceedings 112, May 2022
4. 4Autonomous algorithmic collusion: Q-learning under sequential pricing · Timo Klein, RAND Journal of Economics 52(3), September 2021 (RePEc record and abstract)
5. 5Artificial Intelligence: Can Seemingly Collusive Outcomes Be Avoided? · Abada and Lambin, Management Science 69(9), September 2023 (RePEc record and abstract)
6. 6Algorithmic Collusion by Large Language Models · arXiv (Fish, Gonczarowski and Shorrer), version 6, August 2026
7. 7Algorithmic Pricing and Competition: Empirical Evidence from the German Retail Gasoline Market · Assad, Clark, Ershov and Xu, Journal of Political Economy 132(3), 2024 (RePEc record and abstract)

Where this shows up in our work

• CALIBER, the market testbed for AI agents measures from an AI agent's trades whether it is gullible, herds, overpays, or can be steered.
• LEDGER, auditable Army acquisition decisions turns a trade study into a package where every number cites its source and AI drafts but never decides.