{"paper":{"title":"Continuous-Time Reinforcement Learning for $N$-Player Stochastic Differential Games with Exploratory Policies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jing Zhang, Jisheng Liu","submitted_at":"2026-07-22T09:00:00Z","abstract_excerpt":"We study continuous-time reinforcement learning for $N$-player noncooperative stochastic differential games. Each player adopts an entropy-regularized exploratory policy; given the others' actions, the optimal response is a Gibbs distribution, and a Nash equilibrium requires these $N$ conditional distributions to be jointly compatible. We prove that the natural equilibrium concept -- simultaneous Hamiltonian maximization -- is equivalent to this compatibility, and establish a necessary and sufficient condition expressed as a computable cross-partial criterion on the optimal $q$-functions. Nash"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19928","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.19928/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}