Recovering and Certifying Incentives in Zero-Sum Stopping Games

We study an offline inverse reinforcement learning problem in which either adversarial player can terminate a game by stopping a shared Markov process. A demonstration records which player stopped and where, while the terminal incentives rationalizing these decisions are unknown. Our goal is to recover both players' incentives and the game value and verify whether they implement the observed boundaries within a transfer and smooth-fit class. Local boundary matching is insufficient because both stopping decisions depend on the same continuation value and must remain mutually optimal from every initial state. Our method solves once for the common continuation value between the observed boundaries, recovers both incentives from its boundary values, and applies a global verification step to rule out profitable deviations. We establish necessity, sufficiency, and uniqueness within a smooth-fit class, and characterize stationary contact and dynamics uncertainty through admissible transfer and value sets. Across 24 synthetic games, direct recovery matches converged adaptive calibration without repeated game solves, while a stopping-action IRL baseline evaluates transfer recovery and unilateral deviations. Propagating volatility uncertainty yields certified transfer and value sets at all tested budgets. Each sixteenfold increase in data reduces mean transfer width by about 75%, whereas plug-in sets miss the true transfers. On held-out industry returns with 24 planted contracts, full-path monitoring reduces mean transfer- and value-set widths by 40.3% and 36.7%, respectively.