发表机构
Pusan National University（釜山大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究异构语言模型市场的算法合谋，发现不同模型合谋程度不同，混合市场合谋性变化与模型特性相关，GPT可降低市场合谋性，租金分配与价格主导模型预测一致。
AI 中文摘要
定价算法合谋的证据来自于每个卖家运行相同算法的市场。本文探究当卖家运行的算法不同时会发生什么：在一个四厂商logit伯川德市场中，四家提供商的四款语言模型（均为最低层级）在无沟通的情况下定价，涵盖所有同质、两两组合及完全混合的情况（共11种组合，20次运行，200个周期）。合谋是模型的属性：Claude和Gemini市场达到垄断租金的72%至79%，DeepSeek市场为24%，GPT市场则无合谋，不过GPT价格会偏离垄断水平而非趋近于竞争水平。混合本身不会减少合谋：包含Gemini的市场（以最高价格开盘并稳定在最高水平）比其构建的同质市场更具合谋性；包含Claude的市场（开盘价较低且跟随竞争对手降价）合谋性更低；仅完全混合市场的合谋性显著低于同质市场的平均值。稳定性取决于最不稳定的参与者：两家GPT厂商足以阻止任何市场收敛。在混合市场内部，租金按传递顺序分配：DeepSeek超过Claude超过Gemini超过GPT，这与锚定排名相反。正如价格主导模型所预测，提价的模型收集的租金最少。
英文摘要
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 composi- tion (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 col- lusive 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 de- pends 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.
