{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7O5FSFYFIQVCW3M65CZGOBI2TV","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":"2ce9248f1e6a99267764fbad2ebcb8cf9e8187382bb1a1431dfd600684e79f60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-22T17:35:08Z","title_canon_sha256":"e52eb40ed951336772e61c3ab3c434fa9e6ea54e6e10d8d85990feb20424035e"},"schema_version":"1.0","source":{"id":"1510.06695","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06695","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06695v3","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06695","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"7O5FSFYFIQVC","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7O5FSFYFIQVCW3M6","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7O5FSFYF","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:cc177c5be94b42c7555798ce7a83fa584d8fad2065c7914ab8008d1e69103fe7","target":"graph","created_at":"2026-05-18T01:04:37Z","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":"We study connections between optimistic bilevel programming problems and Generalized Nash Equilibrium Problems (GNEP)s. We remark that, when addressing bilevel problems, we consider the general case in which the lower level program is not assumed to have a unique solution. Inspired by the optimal value approach, we propose a new GNEP model that is closely related to the bilevel program. We provide a complete analysis of the relationship between the \"vertical\" bilevel problem and the corresponding \"horizontal\" (one-level) GNEP model. We define classes of problems for which solutions of the bile","authors_text":"Lorenzo Lampariello, Simone Sagratella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-22T17:35:08Z","title":"A Bridge between Bilevel Programs and Nash Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06695","kind":"arxiv","version":3},"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":"sha256:5214c339167d026d2f6aa3c48529db45ed78e8a03669821faed9964811261a9e","target":"record","created_at":"2026-05-18T01:04:37Z","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":"2ce9248f1e6a99267764fbad2ebcb8cf9e8187382bb1a1431dfd600684e79f60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-10-22T17:35:08Z","title_canon_sha256":"e52eb40ed951336772e61c3ab3c434fa9e6ea54e6e10d8d85990feb20424035e"},"schema_version":"1.0","source":{"id":"1510.06695","kind":"arxiv","version":3}},"canonical_sha256":"fbba591705442a2b6d9ee8b267051a9d703c0c8c28ef8047ebf0d2d24321da43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbba591705442a2b6d9ee8b267051a9d703c0c8c28ef8047ebf0d2d24321da43","first_computed_at":"2026-05-18T01:04:37.774535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:37.774535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3B+hrlLYIsW0hO9fZlShVHV2qCoVCAMTrv/EK1OvalHQMQk4lDVPMdcO+PoDcoyVldl03P3nEPyutBUqegqEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:37.775243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06695","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5214c339167d026d2f6aa3c48529db45ed78e8a03669821faed9964811261a9e","sha256:cc177c5be94b42c7555798ce7a83fa584d8fad2065c7914ab8008d1e69103fe7"],"state_sha256":"1d4376ea10e249aac7d9b4405d78905b952c6c66053e24e4bbdbdee5593abdfe"}