Auditing Algorithmic Collusion from Strategy Graphs

2026-08-07

AI Summary

This study addresses the challenge of detecting algorithmic collusion under realistic regulatory constraints, where authorities have limited access to firms’ algorithms and market data. It proposes a novel method that requires neither historical pricing data, demand estimation, nor competitive benchmarks. By querying firms’ frozen pricing policies, the approach constructs a strategy graph and leverages a complete characterization of Nash equilibria in repeated games to extract key topological features—such as maximum betweenness centrality, attractor in-degree, and average path length—from the graph’s unlabeled structure. The resulting metrics uniquely enable effective identification of collusion among reinforcement learning pricing algorithms based solely on strategy graph topology. Validation on Calvano et al.’s Q-learning and decentralized Q-learning models demonstrates strong correlation with profit-based collusion indices, confirming that the strategy graph encodes robust signals of collusive behavior.

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.

Problem

• algorithmic collusion
• strategy graphs
• auditing
• reinforcement learning
• pricing policies

Innovation

• algorithmic collusion
• strategy graphs
• graph-theoretic features
• reinforcement learning auditing
• Nash equilibrium characterization