{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7QFDBKX25ELW5ZSOVTD4BFDEGN","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":"54a4ef4ccd0c450ee392fe8ae521d0cd44b1839f197d30bbc976255defb27b29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-19T08:46:42Z","title_canon_sha256":"5f21a1fa0ae5ba04e23e39b05faeb1a24841ba484f4a5caf4ec6251bf59e61d8"},"schema_version":"1.0","source":{"id":"1704.05653","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05653","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05653v2","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05653","created_at":"2026-05-18T00:34:57Z"},{"alias_kind":"pith_short_12","alias_value":"7QFDBKX25ELW","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7QFDBKX25ELW5ZSO","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7QFDBKX2","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:39631f1f52a2ca9095222606fdcf86640ca96c0821a710167d8bd7d21820cb13","target":"graph","created_at":"2026-05-18T00:34:57Z","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":"This paper studies the problem of Nash equilibrium approximation in large-scale heterogeneous mean-field games under communication and computation constraints. A deterministic mean-field game is considered in which the non-linear utility function of each agent depends on its action, the average of other agents' actions (called the mean variable of that agent) and a deterministic parameter. It is shown that the equilibrium mean variables of all agents converge uniformly to a constant, called asymptotic equilibrium mean (AEM), as the number of agents tends to infinity. The AEM, which depends on ","authors_text":"Ehsan Nekouei, Girish Nair, Tansu Alpcan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-19T08:46:42Z","title":"Nash Equilibrium Approximation under Communication and Computation Constraints in Large-Scale Non-cooperative Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05653","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":"sha256:39c5d8b9ad36e02076266749c437f5626914e871fb4f1f6dc238318f7feff474","target":"record","created_at":"2026-05-18T00:34:57Z","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":"54a4ef4ccd0c450ee392fe8ae521d0cd44b1839f197d30bbc976255defb27b29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-19T08:46:42Z","title_canon_sha256":"5f21a1fa0ae5ba04e23e39b05faeb1a24841ba484f4a5caf4ec6251bf59e61d8"},"schema_version":"1.0","source":{"id":"1704.05653","kind":"arxiv","version":2}},"canonical_sha256":"fc0a30aafae9176ee64eacc7c09464334c5372559eaf14eed915477dc6647400","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc0a30aafae9176ee64eacc7c09464334c5372559eaf14eed915477dc6647400","first_computed_at":"2026-05-18T00:34:57.320395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:57.320395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g8PmGpb+AjaYaNNyF/Y48L1TnTurK82ie/OCgeZ1yiW7LTmc1wA58Mw9ZfUXauUJe+bedupypv7AQ1RoV9cnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:57.321102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05653","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39c5d8b9ad36e02076266749c437f5626914e871fb4f1f6dc238318f7feff474","sha256:39631f1f52a2ca9095222606fdcf86640ca96c0821a710167d8bd7d21820cb13"],"state_sha256":"25175d3de283e6d46ba49dfdac06f8727096e1ae89c2f718b5ee1d9fca3980d0"}