4diff_bertrand

Description

Evidence that pricing algorithms collude comes from markets in which every seller runs the same algorithm. We ask what happens when they do not. Four language models from four providers, each at its cheapest tier, price in a four-firm logit Bertrand market without communication, in every homogeneous, two-by-two and fully mixed composition (11 cells, 20 runs, 200 periods). Collusion is a property of the model: Claude and Gemini markets reach 72 to 79 percent of the monopoly rent, DeepSeek markets 24 percent, and GPT markets none, though GPT prices drift above the monopoly level rather than toward competition. Mixing does not reduce collusion by itself. Markets containing Gemini, which opens at the highest price and settles highest, are more collusive than the homogeneous markets they are built from; markets containing Claude, which opens lower and follows its rivals down, are less so; and only the fully mixed market is significantly less collusive than the average homogeneous one. Stability depends on the least stable participant: two GPT firms suffice to keep any market from converging. Inside mixed markets the rent is shared in a transitive order, DeepSeek over Claude over Gemini over GPT, that inverts the anchor ranking. The model that raises the price collects the least of the rent, as the price-leadership model predicts.

Institutions

• Pusan National University

  Busan, Busan

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