One Bit Is Enough: Breaking and Auditing Tacit Collusion Between Learning Pricing Agents

Pricing agents can learn to collude without communicating: they settle on high prices and punish rivals who undercut. Using the standard logit-demand market of Calvano et al. (2020), we trained Q-learning agents in about 4,300 sessions while restricting what each agent sees of its rival’s price. We compared them with control agents that reach high prices but cannot sustain collusion. Rounding the rival’s price to one bit (“higher or lower”) barely reduces collusion (index 0.81 → 0.75). Random noise or a single period of delay roughly halves it, and delay removes no information. Collusion is a private convention: agents from different sessions fail to collude together (0.20), but a new entrant re-learns it (0.74). At equal price levels, the evidence auditors usually rely on fails: high prices score at chance (AUC 0.48) and parallel pricing points the wrong way (0.02). Tests of whether a firm reacts to its rival work well (0.90). Reading agents’ learned strategies shows that behaviour can understate collusive intent by half, and is the best detector overall (0.90). The results hold across learning parameters. We release a tested LLM-agent extension with pre-registered predictions.