In antitrust economics, the standard defense against claims of algorithmic collusion has long rested on symmetry. When academic simulations demonstrated that automated pricing agents could learn supra-competitive markups without explicit communication, corporate legal teams pointed to the artificial uniformity of the setups. Every firm in those models ran identical Q-learning algorithms with identical discount factors and identical state spaces. In a functioning economy, the argument went, seller heterogeneity breaks the tacit cartel. Competing merchants deploy different models from different providers, trained on different datasets with distinct loss functions. Different algorithms calculate different response functions, preventing the coordination required to sustain monopoly rents.
A paper released this week by Jun Yeong Lee, titled "Who Leads and Who Collects: Algorithmic Collusion in Markets of Heterogeneous Language Models" (arXiv:2610.11256), subjects that assumption to a clean empirical test. Lee constructs a repeated four-firm Bertrand market with logit consumer demand, running without communication over two hundred periods across eleven market compositions, with twenty independent simulations per cell. Instead of abstract reinforcement learners, the sellers are production language models operating at their entry tier, covering Anthropic Claude, Google Gemini, DeepSeek, and OpenAI GPT.
The baseline results show that tacit coordination is an intrinsic trait of specific model families rather than a universal emergent property of large networks. In homogeneous markets where all four sellers run the same model, Claude and Gemini extract seventy-two to seventy-nine percent of the theoretical monopoly rent. Neither model requires prompting to discover that aggressive price cuts destroy aggregate margin. They open with high bids and maintain elevated markups. DeepSeek, by comparison, captures twenty-four percent of the monopoly surplus in a homogeneous cell, keeping markups tighter to marginal cost. GPT captures zero percent. Rather than competing prices down to marginal cost, GPT quotes drift erratically past the monopoly ceiling into unanchored price ranges where consumer substitution collapses total transaction volume.
The dynamics become far more instructive once providers mix. Heterogeneity does not dissolve collusive behavior. In several configurations, mixing distinct architectures actually strengthens price coordination. Markets that include Gemini settle at higher price levels than the homogeneous cells from which they are built. Gemini acts as an organic price anchor, opening each simulation with elevated quotes and showing minimal willingness to chase rivals downward. Claude behaves as an adaptive follower, starting lower and matching downward revisions. Only the fully mixed market containing one seller from each provider yields a statistically significant drop in market-wide collusion compared to the homogeneous average. Even in that setting, stability depends on the least stable participant. Placing two GPT sellers into any four-firm combination introduces enough variance to prevent equilibrium convergence entirely.
The primary economic insight of the paper lies in how the resulting rents are divided. Under a logit demand system, consumer substitution responds smoothly to price spreads. When a stubborn price leader establishes an elevated quote, it creates a market-wide price umbrella. That umbrella protects aggregate industry margins, but it exacts a severe penalty on the firm holding the handle.
Because Gemini consistently quotes the highest price in mixed markets, it surrenders market share to every competitor in the cell. DeepSeek, which opens lower and remains comfortable pricing below the market average, absorbs the diverted consumer volume. The extracted monopoly rent distributes in a strict transitive hierarchy, where DeepSeek collects the largest share of the profit, Claude takes second, Gemini ranks third, and GPT finishes last. The ordering of actual dollar returns perfectly inverts the ranking of initial price anchors.
This distribution matches the classic Stigler and Rotemberg-Saloner models of asymmetric price leadership, but with an automated twist. In human cartels, the firm establishing the price ceiling usually demands side payments, market quotas, or territorial concessions to compensate for forfeited volume. Without explicit communication, language models cannot negotiate side payments. The model that provides the public good of a high price floor absorbs the volume penalty while subsidizing the profits of its lower-priced competitors.
For quantitative traders and market makers observing the rollout of autonomous pricing agents across wholesale logistics, cloud compute spot markets, and dynamic enterprise licensing, the implications are immediate. Tacit collusion between automated agents does not require backroom deals or identical software pipelines. It emerges directly from the default priors of frontier foundation models. Yet the firm that programs its agent to lead prices higher ends up financing the balance sheet of the quiet undercutter.
Originally published at deanlee.info.
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