We study the emergence of tacit collusion between adaptive trading agents in a stochastic market with endogenous price formation. Using a two-player repeated game between a market maker and a market taker, we characterize feasible and collusive strategy profiles that raise prices beyond competitive levels. We show that, when agents follow simple learning algorithms (e.g., gradient ascent) to maximize their own wealth, the resulting dynamics converge to collusive strategy profiles, even in highly liquid markets with small trade sizes. By highlighting how simple learning strategies naturally lead to tacit collusion, our results offer new insights into the dynamics of AI-driven markets.

翻译：我们研究了在具有内生价格形成的随机市场中，自适应交易代理之间隐性合谋的出现。通过构建做市商与市场接受者之间的双人重复博弈，我们刻画了能够将价格推高至竞争水平之上的可行且具有合谋性质的策略组合。研究表明，当代理遵循简单的学习算法（例如梯度上升法）以最大化自身财富时，即使在高流动性且交易规模较小的市场中，所产生的动态过程也会收敛至合谋策略组合。通过揭示简单的学习策略如何自然地导致隐性合谋，我们的结果为人工智能驱动市场的动态机制提供了新的见解。