Auditing Algorithmic Collusion from Strategy Graphs

Abstract

Detecting algorithmic collusion is challenging because regulators often have limited access to firms' algorithms, training data, and market information. We study an intermediate-information regime in which an auditor can query firms' frozen pricing policies and construct the induced strategy graph. Using a complete characterization of Nash equilibria in a repeated pricing game, we identify graph-theoretic features of strategy graphs that are associated with collusive reward-and-punishment schemes, including maximum betweenness, attractor in-degree, and average path length. We then test these metrics on policies learned by decentralized Q-learning and the Q-learning algorithm of Calvano et al. (2020). We find that especially the maximum betweenness and attractor in-degree are strongly correlated with the standard profit-based Collusion Index. Importantly, the proposed metrics rely only on the unlabeled topology of strategy graphs and require neither price histories, demand estimates, nor competitive and monopoly benchmarks. Our results suggest that the structure of frozen pricing policies contains robust signals of collusion among reinforcement learning algorithms and provides a promising basis for auditing algorithmic pricing systems under limited information.