{"paper":{"title":"Operator approach to values of stochastic games with varying stage duration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Guillaume Vigeral (CEREMADE), Sylvain Sorin (IMJ)","submitted_at":"2015-02-13T14:24:19Z","abstract_excerpt":"We study the links between the values of  stochastic  games   with varying stage duration $h$,  the corresponding  Shapley operators $\\bf{T}$ and ${\\bf{T}}\\_h$and the solution of $\\dot f\\_t = ({\\bf{T}} - Id )f\\_t$. Considering general non expansive maps we establish two kinds of results, under both the discounted or the finite length framework, that apply to the class of \"exact\" stochastic games. First, for a fixed length or discount factor, the value converges as the stage duration go to 0. Second, the asymptotic behavior of the value as the length goes to infinity, or as the discount factor "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04000","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}