When Bodies Commit: Commitment-Grounded Policy Learning in Embodied Games

Embodied agents can remain strategically undecided after their bodies have already made some outcomes physically unreachable. In competitive interaction, this mismatch creates a distinctive vulnerability: an opponent can observe physical commitment and exploit choices that can no longer be reversed. We formalize this phenomenon through continuation capability and develop commitment-grounded policy learning, which adaptively expands both players' high-level strategy sets while keeping the underlying physical skills fixed. Our analysis connects the resulting finite policy-space game to the original embodied interaction, quantifies the approximation induced by a finite responder set, and yields an oracle-based certificate of the remaining strategic gap. On a humanoid–quadruped penalty system, fixed side-blind response sets underestimate learned responders by up to 18% once commitment becomes readable. A controlled game calibrated from the robot measurements reproduces this failure and enables multi-seed evaluation. Across eight seeds, adaptive responder-set expansion consistently improves over one-sided learning, archive-only minimax, and self-play, reducing the worst-case held-out responder payoff by 9% relative to self-play with twice the training budget. These results identify physical commitment as a strategic variable in embodied learning: robustness depends not only on what an agent intends to do, but also on what its body can still do.