{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NIPP4REFQIYEI7VYU4AWZRP5DG","short_pith_number":"pith:NIPP4REF","canonical_record":{"source":{"id":"2505.22909","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.GN","submitted_at":"2025-05-28T22:18:35Z","cross_cats_sorted":["cs.AI","cs.GT","q-fin.EC"],"title_canon_sha256":"9889e1eb9f3c540fa859b9d815ae6c50e76e9cbea3ff038ea8b57fecd1d25bc3","abstract_canon_sha256":"c2ecd0811ee504a1e4add2d1f278c1d26a2915f7d2478ac1c7a536d44f381ee0"},"schema_version":"1.0"},"canonical_sha256":"6a1efe44858230447eb8a7016cc5fd19ba74a8de9af734e058d3425ea8c978fb","source":{"kind":"arxiv","id":"2505.22909","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22909","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22909v1","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22909","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"NIPP4REFQIYE","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"NIPP4REFQIYEI7VY","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"NIPP4REF","created_at":"2026-07-05T11:11:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NIPP4REFQIYEI7VYU4AWZRP5DG","target":"record","payload":{"canonical_record":{"source":{"id":"2505.22909","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.GN","submitted_at":"2025-05-28T22:18:35Z","cross_cats_sorted":["cs.AI","cs.GT","q-fin.EC"],"title_canon_sha256":"9889e1eb9f3c540fa859b9d815ae6c50e76e9cbea3ff038ea8b57fecd1d25bc3","abstract_canon_sha256":"c2ecd0811ee504a1e4add2d1f278c1d26a2915f7d2478ac1c7a536d44f381ee0"},"schema_version":"1.0"},"canonical_sha256":"6a1efe44858230447eb8a7016cc5fd19ba74a8de9af734e058d3425ea8c978fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:51.696352Z","signature_b64":"WvFBfsVb05A/3RDeKLc+hiX2Os1Lqqr1p+jelqsfD2fDVHTzV7pWbChnfXplflbf1Mnoao6EdC1dgqvGEk0vAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a1efe44858230447eb8a7016cc5fd19ba74a8de9af734e058d3425ea8c978fb","last_reissued_at":"2026-07-05T11:11:51.695843Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:51.695843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.22909","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0NUtfmC3/g2AygDRLZXJBq5W4PWHHc0ftuCHBSMVqPr7kvKyceBVAgi030X0pI2iX3F+HmIopUipFl2VWgrlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:39:27.015016Z"},"content_sha256":"d56c680cdfda882f51a5702cf723fb8cf6bb66ca43e503771d9a67e86065e4df","schema_version":"1.0","event_id":"sha256:d56c680cdfda882f51a5702cf723fb8cf6bb66ca43e503771d9a67e86065e4df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NIPP4REFQIYEI7VYU4AWZRP5DG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning to Charge More: A Theoretical Study of Collusion by Q-Learning Agents","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.GT","q-fin.EC"],"primary_cat":"econ.GN","authors_text":"Cristian Chica, Gilad Lerman, Yinglong Guo","submitted_at":"2025-05-28T22:18:35Z","abstract_excerpt":"There is growing experimental evidence that $Q$-learning agents may learn to charge supracompetitive prices. We provide the first theoretical explanation for this behavior in infinite repeated games. Firms update their pricing policies based solely on observed profits, without computing equilibrium strategies. We show that when the game admits both a one-stage Nash equilibrium price and a collusive-enabling price, and when the $Q$-function satisfies certain inequalities at the end of experimentation, firms learn to consistently charge supracompetitive prices. We introduce a new class of one-me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22909","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.22909/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:11:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zegvnAS5rCbWMZ13M0QPntSPrLgEol7qab42vDG7CfAFC6bK6v6Rr9aWPQ0wRPL0OnumP76zi5zEUaGlsbU2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T09:39:27.015763Z"},"content_sha256":"5e3f304caa3122f773dab90d6c9f62fef10095fbcdc6876e710fdf72456a06a6","schema_version":"1.0","event_id":"sha256:5e3f304caa3122f773dab90d6c9f62fef10095fbcdc6876e710fdf72456a06a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NIPP4REFQIYEI7VYU4AWZRP5DG/bundle.json","state_url":"https://pith.science/pith/NIPP4REFQIYEI7VYU4AWZRP5DG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NIPP4REFQIYEI7VYU4AWZRP5DG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T09:39:27Z","links":{"resolver":"https://pith.science/pith/NIPP4REFQIYEI7VYU4AWZRP5DG","bundle":"https://pith.science/pith/NIPP4REFQIYEI7VYU4AWZRP5DG/bundle.json","state":"https://pith.science/pith/NIPP4REFQIYEI7VYU4AWZRP5DG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NIPP4REFQIYEI7VYU4AWZRP5DG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NIPP4REFQIYEI7VYU4AWZRP5DG","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":"c2ecd0811ee504a1e4add2d1f278c1d26a2915f7d2478ac1c7a536d44f381ee0","cross_cats_sorted":["cs.AI","cs.GT","q-fin.EC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.GN","submitted_at":"2025-05-28T22:18:35Z","title_canon_sha256":"9889e1eb9f3c540fa859b9d815ae6c50e76e9cbea3ff038ea8b57fecd1d25bc3"},"schema_version":"1.0","source":{"id":"2505.22909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22909","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22909v1","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22909","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"NIPP4REFQIYE","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_16","alias_value":"NIPP4REFQIYEI7VY","created_at":"2026-07-05T11:11:51Z"},{"alias_kind":"pith_short_8","alias_value":"NIPP4REF","created_at":"2026-07-05T11:11:51Z"}],"graph_snapshots":[{"event_id":"sha256:5e3f304caa3122f773dab90d6c9f62fef10095fbcdc6876e710fdf72456a06a6","target":"graph","created_at":"2026-07-05T11:11:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.22909/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There is growing experimental evidence that $Q$-learning agents may learn to charge supracompetitive prices. We provide the first theoretical explanation for this behavior in infinite repeated games. Firms update their pricing policies based solely on observed profits, without computing equilibrium strategies. We show that when the game admits both a one-stage Nash equilibrium price and a collusive-enabling price, and when the $Q$-function satisfies certain inequalities at the end of experimentation, firms learn to consistently charge supracompetitive prices. We introduce a new class of one-me","authors_text":"Cristian Chica, Gilad Lerman, Yinglong Guo","cross_cats":["cs.AI","cs.GT","q-fin.EC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.GN","submitted_at":"2025-05-28T22:18:35Z","title":"Learning to Charge More: A Theoretical Study of Collusion by Q-Learning Agents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22909","kind":"arxiv","version":1},"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:d56c680cdfda882f51a5702cf723fb8cf6bb66ca43e503771d9a67e86065e4df","target":"record","created_at":"2026-07-05T11:11:51Z","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":"c2ecd0811ee504a1e4add2d1f278c1d26a2915f7d2478ac1c7a536d44f381ee0","cross_cats_sorted":["cs.AI","cs.GT","q-fin.EC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.GN","submitted_at":"2025-05-28T22:18:35Z","title_canon_sha256":"9889e1eb9f3c540fa859b9d815ae6c50e76e9cbea3ff038ea8b57fecd1d25bc3"},"schema_version":"1.0","source":{"id":"2505.22909","kind":"arxiv","version":1}},"canonical_sha256":"6a1efe44858230447eb8a7016cc5fd19ba74a8de9af734e058d3425ea8c978fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a1efe44858230447eb8a7016cc5fd19ba74a8de9af734e058d3425ea8c978fb","first_computed_at":"2026-07-05T11:11:51.695843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:51.695843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WvFBfsVb05A/3RDeKLc+hiX2Os1Lqqr1p+jelqsfD2fDVHTzV7pWbChnfXplflbf1Mnoao6EdC1dgqvGEk0vAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:51.696352Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d56c680cdfda882f51a5702cf723fb8cf6bb66ca43e503771d9a67e86065e4df","sha256:5e3f304caa3122f773dab90d6c9f62fef10095fbcdc6876e710fdf72456a06a6"],"state_sha256":"b14998b6c5b20cd7f2d53f45a09a25d8d2900b0786089bf7f79baefda66d1864"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Pn1qJaK/VPcebTj+d0kPFZdAbIOVYVt4jGtyzbEcBr4m10FoEJtiNmxYT8pIK8tWymjaajY5GosDV7P8ZOYDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T09:39:27.021088Z","bundle_sha256":"95c1839cb4a0aa3237128d7d533e45def37fb94bdf3162f521910f6c50a7d161"}}