Adaptive Algorithms, Tacit Collusion, and Design for Competition

Empirical and experimental evidence shows artificial intelligence algorithms learn to charge supracompetitive prices. In this paper we develop a theoretical model to study collusion by adaptive learning algorithms. With a fluid approximation technique, we characterize the learning outcomes in continuous time for general games and identify collusion's main driver: the coordination bias. In a simple dominant strategy game, we show how correlation between algorithms' estimates leads to persistent bias, sustaining collusive actions in the long run. We prove that algorithms using counterfactual returns to inform their updates avoid this bias and converge to dominant strategies. We design a mechanism with feedback: the designer reveals ex-post information to help counterfactual computations. We show that this mechanism implements the social optimum. Finally, we apply our framework to two simulations of price competition and auctions studied in the literature and rationalize analytically the results.