{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4UQVFAGYVEEEVNTMNGTPDC4ZHV","short_pith_number":"pith:4UQVFAGY","schema_version":"1.0","canonical_sha256":"e5215280d8a9084ab66c69a6f18b993d6e1fcaf1a9710630c4682222e5ee344a","source":{"kind":"arxiv","id":"1612.07878","version":2},"attestation_state":"computed","paper":{"title":"Markov-Nash Equilibria in Mean-Field Games with Discounted Cost","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SY","authors_text":"Maxim Raginsky, Naci Saldi, Tamer Ba\\c{s}ar","submitted_at":"2016-12-23T05:34:28Z","abstract_excerpt":"In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish space. At each time, the agents are coupled through the empirical distribution of their states, which affects both the agents' individual costs and their state transition probabilities. We introduce a new solution concept of the Markov-Nash equilibrium, under which a policy is player-by-player optimal in the class of all Markov policies. Under mild assumptio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.07878","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-12-23T05:34:28Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"16e9f43880a072a22bc1d5c75639fdd068d3e69e236e1c3c8a2a5f80fbdea3f0","abstract_canon_sha256":"788820e0493884844e795bfad8814a55676baa7e81ee36b3c29c96119681a334"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:49.133778Z","signature_b64":"Mfv4fzFG3kF0d0ENe1EjETz2bRYaaqK4kRnINz2qmWBNMNGY7zg2+qcMeZi8X5zlLc2Ifk2jro55heubmEe4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5215280d8a9084ab66c69a6f18b993d6e1fcaf1a9710630c4682222e5ee344a","last_reissued_at":"2026-05-18T00:52:49.133147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:49.133147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Markov-Nash Equilibria in Mean-Field Games with Discounted Cost","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SY","authors_text":"Maxim Raginsky, Naci Saldi, Tamer Ba\\c{s}ar","submitted_at":"2016-12-23T05:34:28Z","abstract_excerpt":"In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish space. At each time, the agents are coupled through the empirical distribution of their states, which affects both the agents' individual costs and their state transition probabilities. We introduce a new solution concept of the Markov-Nash equilibrium, under which a policy is player-by-player optimal in the class of all Markov policies. Under mild assumptio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07878","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.07878","created_at":"2026-05-18T00:52:49.133236+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.07878v2","created_at":"2026-05-18T00:52:49.133236+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07878","created_at":"2026-05-18T00:52:49.133236+00:00"},{"alias_kind":"pith_short_12","alias_value":"4UQVFAGYVEEE","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4UQVFAGYVEEEVNTM","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4UQVFAGY","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4UQVFAGYVEEEVNTMNGTPDC4ZHV","json":"https://pith.science/pith/4UQVFAGYVEEEVNTMNGTPDC4ZHV.json","graph_json":"https://pith.science/api/pith-number/4UQVFAGYVEEEVNTMNGTPDC4ZHV/graph.json","events_json":"https://pith.science/api/pith-number/4UQVFAGYVEEEVNTMNGTPDC4ZHV/events.json","paper":"https://pith.science/paper/4UQVFAGY"},"agent_actions":{"view_html":"https://pith.science/pith/4UQVFAGYVEEEVNTMNGTPDC4ZHV","download_json":"https://pith.science/pith/4UQVFAGYVEEEVNTMNGTPDC4ZHV.json","view_paper":"https://pith.science/paper/4UQVFAGY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.07878&json=true","fetch_graph":"https://pith.science/api/pith-number/4UQVFAGYVEEEVNTMNGTPDC4ZHV/graph.json","fetch_events":"https://pith.science/api/pith-number/4UQVFAGYVEEEVNTMNGTPDC4ZHV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4UQVFAGYVEEEVNTMNGTPDC4ZHV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4UQVFAGYVEEEVNTMNGTPDC4ZHV/action/storage_attestation","attest_author":"https://pith.science/pith/4UQVFAGYVEEEVNTMNGTPDC4ZHV/action/author_attestation","sign_citation":"https://pith.science/pith/4UQVFAGYVEEEVNTMNGTPDC4ZHV/action/citation_signature","submit_replication":"https://pith.science/pith/4UQVFAGYVEEEVNTMNGTPDC4ZHV/action/replication_record"}},"created_at":"2026-05-18T00:52:49.133236+00:00","updated_at":"2026-05-18T00:52:49.133236+00:00"}