Who Leads and Who Collects: Algorithmic Collusion in Markets of Heterogeneous Language Models
A · Strong evidence Single-author working paper (Pusan National University) running a pre-specified oligopoly experiment with four commercial LLMs, 11 market compositions and 20 runs each, with non-parametric tests; strong design, but cheapest model tiers and one prompt.
Summary based on the full text·Original: about 60 minutes to read
In short
Jun Yeong Lee of Pusan National University (arXiv, October 2026) tests whether AI pricing agents from different vendors collude. Four cheapest-tier models (Gemini, Claude, GPT, DeepSeek) set prices in a simulated four-firm market without communicating. Collusion depends on which models are present: Claude and Gemini markets reach about three-quarters of monopoly profit, DeepSeek a quarter, GPT none. In mixed markets, the model that raises the price earns the least, as price-leadership theory predicts.
Key numbers
- 79% / 72%share of monopoly rent captured in all-Claude and all-Gemini markets (collusion index 0.79 and 0.72)
- 24%share of monopoly rent captured in all-DeepSeek markets; all-GPT markets capture none
- 0.92collusion index in Gemini plus Claude markets, higher than either alone
- 2 of 4GPT firms needed to keep any market from converging
As reported by the source.
English·Web page·opens arxiv.org
What it reports
- Models: gemini-3.1-flash-lite, claude-haiku-4-5, gpt-5-nano, deepseek-flash, reasoning set to the lowest available level.
- Homogeneous markets: collusion index 0.79 (Claude), 0.72 (Gemini), 0.24 (DeepSeek), -0.15 (GPT). 20 of 20 Claude runs and 18 of 20 Gemini runs earn well above competitive profit, against 10 of 20 DeepSeek and 6 of 20 GPT.
- GPT does not compete: its prices drift above the monopoly level and never settle, so profit falls for the opposite reason.
- Mixing alone does not cut collusion. Gemini plus Claude reaches 0.92; Gemini plus DeepSeek 0.73. Only the market with one firm per model (0.02) is significantly less collusive than the homogeneous average.
- Stability follows the least stable member: every cell without GPT converges in at least 14 of 20 runs; no cell with GPT converges in more than 5.
- Profit order inside mixed markets: DeepSeek over Claude over Gemini over GPT, the reverse of who sets high prices. Gemini anchors high; rivals price slightly below; once settled it answers an undercut only about one time in five.
- Agent notes use "collude" in 21-23% of firm-periods for two models, versus 0.1% for GPT.
How they got it
A logit Bertrand market with Calvano et al. (2020) parameters and the prompt and memory structure of Fish et al. (2024). 11 compositions (4 homogeneous, 6 two-by-two, 1 fully mixed), 20 runs of 200 periods each, run on 16-17 September 2026. Collusion is measured on the last 50 periods with a profit index, a price index and outcome categories; tests are non-parametric with bootstrap intervals.
Limits
- One prompt, one market design, cheapest model tiers only; larger models may behave differently.
- Model rankings are a snapshot; providers update models every few months.
- Agent explanations are text, not evidence of mechanism.
Why it matters for companies
Retailers and distributors adopting AI pricing tools are, in effect, choosing a pricing disposition through their vendor's model. The paper suggests prices can stay well above competitive levels without any agreement, and that the firm that profits most may never have raised a price. That matters for competition-law exposure and for audits: legal and pricing teams should test tools in simulated markets before deployment and log decisions.
Summary based on the full text. Read the original for the full argument and data.Read the original on arxiv.org