{"paper":{"title":"A Nested Family of $k$-total Effective Rewards for Positional Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.DM","authors_text":"Endre Boros, Kazuhisa Makino, Khaled Elbassioni, Vladimir Gurvich","submitted_at":"2014-11-20T09:28:24Z","abstract_excerpt":"We consider Gillette's two-person zero-sum stochastic games with perfect information. For each $k \\in \\ZZ_+$ we introduce an effective reward function, called $k$-total. For $k = 0$ and $1$ this function is known as {\\it mean payoff} and {\\it total reward}, respectively. We restrict our attention to the deterministic case. For all $k$, we prove the existence of a saddle point which can be realized by uniformly optimal pure stationary strategies. We also demonstrate that $k$-total reward games can be embedded into $(k+1)$-total reward games."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6072","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"}