Algorithmic Collusion Without Deterrence: Auditing the Punishment Mechanism in Q-Learning Pricing Agents
Independent tabular Q-learning agents repricing in a simulated Bertrand duopoly converge to supracompetitive prices, and the seminal evidence attributes this to a learned reward-punishment scheme: undercut your rival and it retaliates, so deviation never pays. This mechanistic reading is what turns high prices into a cartel, and into a regulatory target. We replicate the environment of Calvano et al. (2020) and confirm their impulse-response pattern within co-trained pairs. We then audit the pattern on frozen policies, with learning off, and find that on its own it does not identify a mechanism: the return is over-determined rather than selective. In nine of ten converged pairs (914 of 1,024) a single attractor's basin is the entire state space, so every perturbation returns whatever provoked it, and a forced price increase triggers the same retaliatory pattern as an undercut. What co-training produces is a narrow, dyad-specific basin of attraction: re-match frozen agents from independent runs, as Calvano et al. did with learning on, and coordination collapses by 80% with nothing carried across. The deterrence claim is incomplete on its own terms: the one-period undercut of Calvano et al.'s impulse-response test is unprofitable, which we confirm in 92% of pairs, but the optimal deviation, computed by dynamic programming against each partner's frozen strategy, profits by 17.5% on average. The scheme deters only the deviation no optimizer would choose; collusion survives because deviation is never tried, not because it would not pay. Supracompetitive prices are robust; the punishment mechanism read into them does not survive these tests, which changes what the standard test of algorithmic collusion establishes, and what pairing-disruption remedies can be expected to do.