{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NXPHTEIDZLSD3R5ZV46TKCF4QG","short_pith_number":"pith:NXPHTEID","schema_version":"1.0","canonical_sha256":"6dde799103cae43dc7b9af3d3508bc81b85c497727314e63623daacd0be23ba8","source":{"kind":"arxiv","id":"1410.5231","version":2},"attestation_state":"computed","paper":{"title":"General limit value in zero-sum stochastic games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bruno Ziliotto","submitted_at":"2014-10-20T11:32:43Z","abstract_excerpt":"Bewley and Kohlberg (1976) and Mertens and Neyman (1981) have proved, respectively, the existence of the asymptotic value and the uniform value in zero-sum stochastic games with finite state space and finite action sets. In their work, the total payoff in a stochastic game is defined either as a Cesaro mean or an Abel mean of the stage payoffs. This paper presents two findings: first, we generalize the result of Bewley and Kohlberg to a more general class of payoff evaluations and we prove with a counterexample that this result is tight. We also investigate the particular case of absorbing gam"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1410.5231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-20T11:32:43Z","cross_cats_sorted":[],"title_canon_sha256":"b9ab23bf9faed5e1dd0ee67668120e9d1386980eb5149ec5d2fcf6be1fe9f8af","abstract_canon_sha256":"8fe0c1c70c39bb8ba5c51be3c48f879e043c42e724bfdbae43833dd594b400b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:15.279100Z","signature_b64":"YgPIx2Vb1I/GhmzE/nY7Z6mJuSap9VY8LA35WLZ2/2Eehnvv/UEaRyPEmy2woCQSJqXsyKiso6/dqHoVLwNuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dde799103cae43dc7b9af3d3508bc81b85c497727314e63623daacd0be23ba8","last_reissued_at":"2026-05-18T01:27:15.278447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:15.278447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"General limit value in zero-sum stochastic games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bruno Ziliotto","submitted_at":"2014-10-20T11:32:43Z","abstract_excerpt":"Bewley and Kohlberg (1976) and Mertens and Neyman (1981) have proved, respectively, the existence of the asymptotic value and the uniform value in zero-sum stochastic games with finite state space and finite action sets. In their work, the total payoff in a stochastic game is defined either as a Cesaro mean or an Abel mean of the stage payoffs. This paper presents two findings: first, we generalize the result of Bewley and Kohlberg to a more general class of payoff evaluations and we prove with a counterexample that this result is tight. We also investigate the particular case of absorbing gam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5231","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.5231","created_at":"2026-05-18T01:27:15.278540+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.5231v2","created_at":"2026-05-18T01:27:15.278540+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5231","created_at":"2026-05-18T01:27:15.278540+00:00"},{"alias_kind":"pith_short_12","alias_value":"NXPHTEIDZLSD","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NXPHTEIDZLSD3R5Z","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NXPHTEID","created_at":"2026-05-18T12:28:41.024544+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NXPHTEIDZLSD3R5ZV46TKCF4QG","json":"https://pith.science/pith/NXPHTEIDZLSD3R5ZV46TKCF4QG.json","graph_json":"https://pith.science/api/pith-number/NXPHTEIDZLSD3R5ZV46TKCF4QG/graph.json","events_json":"https://pith.science/api/pith-number/NXPHTEIDZLSD3R5ZV46TKCF4QG/events.json","paper":"https://pith.science/paper/NXPHTEID"},"agent_actions":{"view_html":"https://pith.science/pith/NXPHTEIDZLSD3R5ZV46TKCF4QG","download_json":"https://pith.science/pith/NXPHTEIDZLSD3R5ZV46TKCF4QG.json","view_paper":"https://pith.science/paper/NXPHTEID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.5231&json=true","fetch_graph":"https://pith.science/api/pith-number/NXPHTEIDZLSD3R5ZV46TKCF4QG/graph.json","fetch_events":"https://pith.science/api/pith-number/NXPHTEIDZLSD3R5ZV46TKCF4QG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NXPHTEIDZLSD3R5ZV46TKCF4QG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NXPHTEIDZLSD3R5ZV46TKCF4QG/action/storage_attestation","attest_author":"https://pith.science/pith/NXPHTEIDZLSD3R5ZV46TKCF4QG/action/author_attestation","sign_citation":"https://pith.science/pith/NXPHTEIDZLSD3R5ZV46TKCF4QG/action/citation_signature","submit_replication":"https://pith.science/pith/NXPHTEIDZLSD3R5ZV46TKCF4QG/action/replication_record"}},"created_at":"2026-05-18T01:27:15.278540+00:00","updated_at":"2026-05-18T01:27:15.278540+00:00"}