{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PCFVAEANAOQCKOGADTF3PIGB3G","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5482d65a46f2d88d3b3e9e141788deed10a48788c1cc296d3c3a3b5ade037464","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-17T23:00:00Z","title_canon_sha256":"cfc125b7a42894738ffabbe007658f9f2c4a7d18bd83c1632eac1cae182238b9"},"schema_version":"1.0","source":{"id":"1711.06760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06760","created_at":"2026-05-18T00:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06760v1","created_at":"2026-05-18T00:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06760","created_at":"2026-05-18T00:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"PCFVAEANAOQC","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PCFVAEANAOQCKOGA","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PCFVAEAN","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:0ad3d294a609c9bcbded4a12e4a936e9e7bc3b328b631529d2a238c4570d7e0d","target":"graph","created_at":"2026-05-18T00:30:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For the classical backward induction algorithm, the input is an arbitrary $n$-person positional game with perfect information modeled by a finite acyclic directed graph (digraph) and the output is a profile $(x_1, \\ldots, x_n)$ of pure positional strategies that form some special subgame perfect Nash equilibrium. We extend this algorithm to work with digraphs that may have directed cycles. Each digraph admits a unique partition into strongly connected components, which will be treated as the outcomes of the game. Such a game will be called a {\\em deterministic graphical multistage}(DGMS) game.","authors_text":"Vladimir Gurvich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-17T23:00:00Z","title":"Backward induction in presence of cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06760","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c2157e893c6f84862edfeaaaa77355ea3ce64b2df0d6e424aa5a2216c155d91c","target":"record","created_at":"2026-05-18T00:30:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5482d65a46f2d88d3b3e9e141788deed10a48788c1cc296d3c3a3b5ade037464","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-17T23:00:00Z","title_canon_sha256":"cfc125b7a42894738ffabbe007658f9f2c4a7d18bd83c1632eac1cae182238b9"},"schema_version":"1.0","source":{"id":"1711.06760","kind":"arxiv","version":1}},"canonical_sha256":"788b50100d03a02538c01ccbb7a0c1d9af41d7cd0dd3857f82206cee1bfade21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"788b50100d03a02538c01ccbb7a0c1d9af41d7cd0dd3857f82206cee1bfade21","first_computed_at":"2026-05-18T00:30:15.696787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:15.696787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lHBvVaNo0zwPKqaHASoDfqfc/Wi+c66Qe3/r9WipFH2sSpCBe6WpoVyrLuchLnnI2CZq55nyZeDs2tzzNCoABw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:15.697483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2157e893c6f84862edfeaaaa77355ea3ce64b2df0d6e424aa5a2216c155d91c","sha256:0ad3d294a609c9bcbded4a12e4a936e9e7bc3b328b631529d2a238c4570d7e0d"],"state_sha256":"dd041af040ba31ec6762d06f5a1ff44221bc9a5444681c2088f81181cffdd490"}