{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GNXHBWJTQFPLI452THBDUS5QYS","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":"16966c0815d08d5812ee1ae3379ccd6948fe49dcc2a23e95331dc04afe0d8e2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-05-09T23:51:47Z","title_canon_sha256":"1769743ca2616d780c02286d0a5e60d0d9fe6c62574b53322d00c341c6326525"},"schema_version":"1.0","source":{"id":"1105.1824","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1824","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1824v2","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1824","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"GNXHBWJTQFPL","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GNXHBWJTQFPLI452","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GNXHBWJT","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:939ea818fbbbaf5c4c3bc86367d80ae77f9d0b9376ae99f0e096dcddb6871754","target":"graph","created_at":"2026-05-18T04:07:06Z","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 consider coalition formation games in which each player has preferences over the other players and his preferences over coalitions are based on the best player ($\\mathcal{B}$-/B-hedonic games) or the worst player ($\\mathcal{W}$/W-hedonic games) in the coalition. We show that for $\\mathcal{B}$-hedonic games, an individually stable partition is guaranteed to exist and can be computed efficiently. Similarly, there exists a polynomial-time algorithm which returns a Nash stable partition (if one exists) for $\\mathcal{B}$-hedonic games with strict preferences. Both $\\mathcal{W}$- and W-hedonic ga","authors_text":"Evangelia Pyrga, Haris Aziz, Paul Harrenstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-05-09T23:51:47Z","title":"Individual-based stability in hedonic games depending on the best or worst players"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1824","kind":"arxiv","version":2},"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":"sha256:71be1827104888934509752dc727985b349f1b23278fa1d75d90c64d93265118","target":"record","created_at":"2026-05-18T04:07:06Z","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":"16966c0815d08d5812ee1ae3379ccd6948fe49dcc2a23e95331dc04afe0d8e2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-05-09T23:51:47Z","title_canon_sha256":"1769743ca2616d780c02286d0a5e60d0d9fe6c62574b53322d00c341c6326525"},"schema_version":"1.0","source":{"id":"1105.1824","kind":"arxiv","version":2}},"canonical_sha256":"336e70d933815eb473ba99c23a4bb0c4991007a8f0bc323f02bae1354106656f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"336e70d933815eb473ba99c23a4bb0c4991007a8f0bc323f02bae1354106656f","first_computed_at":"2026-05-18T04:07:06.661189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:06.661189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E5u17ivaVf4v4OJUpbhcTDFl9MJSjkEdolnPOdqp258NOB9nx3uhDtnmwk6E/jdGMWqG43RLYIgBaH3V9PhmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:06.661708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1824","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71be1827104888934509752dc727985b349f1b23278fa1d75d90c64d93265118","sha256:939ea818fbbbaf5c4c3bc86367d80ae77f9d0b9376ae99f0e096dcddb6871754"],"state_sha256":"21ee57f013c4677cfb07c2cc06d09714ce987fc3015d5f63f3fd012a91a3e78e"}