We develop a tractable model for studying strategic interactions between learning algorithms. We uncover a mechanism responsible for the emergence of algorithmic collusion. We observe that algorithms periodically coordinate on actions that are more profitable than static Nash equilibria. This novel collusive channel relies on an endogenous statistical linkage in the algorithms' estimates which we call spontaneous coupling. The model's parameters predict whether the statistical linkage will appear, and what market structures facilitate algorithmic collusion. We show that spontaneous coupling can sustain collusion in prices and market shares, complementing experimental findings in the literature. Finally, we apply our results to design algorithmic markets.

翻译：我们开发了一个可处理的模型，用于研究学习算法之间的战略互动。我们揭示了一种导致算法合谋产生的机制。观察到算法会周期性地协调采取比静态纳什均衡更有利可图的行动。这种新颖的合谋渠道依赖于算法估计中一种内生的统计关联，我们称之为自发耦合。模型的参数能够预测这种统计关联是否会出现，以及哪些市场结构会促进算法合谋。我们证明，自发耦合能够维持价格和市场份额上的合谋，补充了文献中的实验发现。最后，我们将研究结果应用于算法市场的设计。