{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZV4ODXZUMDU4CBTDA7LN2F7GHU","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":"bd51baf6cc034fa226d49c9c173f620669cf65a1ce4db7082c1019369e1d4946","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2010-01-21T22:25:21Z","title_canon_sha256":"d7c070a9014102ae69b3ecf16dcf261f647f0fdd906e6bb4b88eef5f28a3a9ca"},"schema_version":"1.0","source":{"id":"1001.3896","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3896","created_at":"2026-05-18T04:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3896v4","created_at":"2026-05-18T04:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3896","created_at":"2026-05-18T04:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"ZV4ODXZUMDU4","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZV4ODXZUMDU4CBTD","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZV4ODXZU","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:535e0637e66e124a9916cd8c9afd0d26d795b07c1730ab191c515fc2a734e125","target":"graph","created_at":"2026-05-18T04:02:50Z","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":"Within the context of games on networks S. Goyal (Goya (2007), pg. 39) posed the following problem. Under any arbitrary but fixed topology, does there exist at least one pure Nash equilibrium that exhibits a positive relation between the cardinality of a player's set of neighbors and its utility payoff? In this paper we present a class of topologies/games in which pure Nash equilibria with the above property do not exist.","authors_text":"Ali Kakhbod, Demosthenis Teneketzis","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2010-01-21T22:25:21Z","title":"Games on Social Networks: On a Problem Posed by Goyal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3896","kind":"arxiv","version":4},"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":"sha256:719823a4c223365de5768ca19dc2f6d5b823ceb2f24b128a4c4a20bbe129c99f","target":"record","created_at":"2026-05-18T04:02:50Z","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":"bd51baf6cc034fa226d49c9c173f620669cf65a1ce4db7082c1019369e1d4946","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2010-01-21T22:25:21Z","title_canon_sha256":"d7c070a9014102ae69b3ecf16dcf261f647f0fdd906e6bb4b88eef5f28a3a9ca"},"schema_version":"1.0","source":{"id":"1001.3896","kind":"arxiv","version":4}},"canonical_sha256":"cd78e1df3460e9c1066307d6dd17e63d10fbcdf9406ceb325c96cfbc8998d117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd78e1df3460e9c1066307d6dd17e63d10fbcdf9406ceb325c96cfbc8998d117","first_computed_at":"2026-05-18T04:02:50.667070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:50.667070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"afJaPpgTH7LPGsV2IUwuZ/mLinQnAUZYKxq72zWgx383FdC/VFR258KWEdU87PjMglvzmFyxg9YvyPhY+mC2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:50.667886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.3896","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:719823a4c223365de5768ca19dc2f6d5b823ceb2f24b128a4c4a20bbe129c99f","sha256:535e0637e66e124a9916cd8c9afd0d26d795b07c1730ab191c515fc2a734e125"],"state_sha256":"cda2e9a1e674ea22d03188e3a92d59920ef55e96c320422214dfc79cf0c6bf8f"}