The Stable Discriminant and Adaptive Guards for Auditing Stable Matchings

Auditing a proposed matching need not recover every preference sign. We derive bilateral Gaussian audit games for scalar queries and matching-feasible feedback. The stable game is a concave design over doubly stochastic exposures; a fixed blocker is optimally tested by mixing the proposed matching with a partner swap. Adaptive guards reject a pair as soon as one endpoint suffices, without learning redundant near ties, and are optimal up to logarithmic factors in finite expected deployment rounds. Separate information tracking attains the asymptotic leading constant. A witness-local likelihood boundary removes unnecessary full-market stopping overhead. Concavity yields an assignment-based numerical design check, and confidence envelopes convert it into a simultaneous guarantee for the unknown information rate and an adaptively selected exposure. Implemented trackers, guards, and repeated-look design checks distinguish deployment rounds, scalar observations, numerical error, and statistical uncertainty. Target-separation examples show why auditing, finding an optimal matching, and learning all stable pairs have different information costs.