We study the emergence of tacit collusion in a repeated game between a market maker, who controls market liquidity, and a market taker, who chooses trade quantities. The market price evolves according to the endogenous price impact of trades and exogenous innovations to economic fundamentals. We define collusion as persistent overpricing over economic fundamentals and characterize the set of feasible and collusive strategy profiles. Our main result shows that a broad class of simple learning dynamics, including gradient ascent updates, converges in finite time to collusive strategies when the agents maximize individual wealth, defined as the value of their portfolio, without any explicit coordination. The key economic mechanism is that when aggregate supply in the market is positive, overpricing raises the market capitalization and thus the total wealth of market participants, inducing a cooperative component in otherwise non-cooperative learning objectives. These results identify an inherent structure through which decentralized learning by AI-driven agents can autonomously generate persistent overpricing in financial markets.

翻译：我们研究市场做市商（控制市场流动性）与市场交易者（选择交易数量）在重复博弈中隐性合谋的出现。市场价格根据交易的内生价格冲击和经济基本面的外生创新而演变。我们将合谋定义为持续高于经济基本面的定价，并刻画了可行且具有合谋性质的策略组合集合。主要结果表明，当代理以最大化个人财富（定义为其投资组合价值）为目标且无需显式协调时，包括梯度上升更新在内的广泛简单学习动态类会在有限时间内收敛至合谋策略。关键经济机制在于：当市场总供给为正时，高价会提高市值从而增加市场参与者的总财富，这在原本非合作的学习目标中引入了合作成分。这些结果揭示了一种内在结构，通过该结构，由人工智能驱动的代理进行去中心化学习能够自主地在金融市场中产生持续性高价现象。