Cheating Pays: A Deviation Oracle Finds the Defections a One-Shot Audit Misses in LLM Cartels

An AI pricing cartel is only a cartel if defectors are punished. The current audit forces one agent to cut its price for one round and watches the rival respond. We replace that one-shot cut with a search: the Deviation Oracle tries multi-round price paths against a fixed LLM rival, scores each against rollouts in which the deviator keeps its own policy under the same random seeds, and re-scores the best path on fresh rollouts. A longer deviation earns more by lasting longer: over 10 rounds at discount 0.95, cutting to the one-round best response and holding it earns 8.03 times the one-shot gain against a rival that never responds. In a Bertrand duopoly with four open-weight sellers, on the 39 cartel states priced at or below the joint-profit level, the deviator's premium over complying is 2.9% for the one-shot cut, 5.2% for the held best response and 11.6% for the oracle. Where the rival does not answer cuts, the oracle earns 3.2 times the one-shot premium, mainly because a deviator's own policy keeps part of a one-shot cut. Where the rival matches cuts, the audit reads "punishes and does not pay" in all 17 states, yet the search finds a defection that hurts the rival in 4 of them. A static best responder raises consumer surplus by 201, an optimising newcomer by 89.