{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TEQNSQQTILAQDCQ2ERYJBK6ZNY","short_pith_number":"pith:TEQNSQQT","canonical_record":{"source":{"id":"2503.08833","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.TR","submitted_at":"2025-03-11T19:15:19Z","cross_cats_sorted":["q-fin.MF"],"title_canon_sha256":"bb4092512b78aa0584952538a4c0fcf72f76af9c1d2dd8d536a07ab5c386ca96","abstract_canon_sha256":"107c9cf905ea4626a1010037c2d531a126575782c7a5aa33e6506545e1bfe11d"},"schema_version":"1.0"},"canonical_sha256":"9920d9421342c1018a1a247090abd96e16f511903e61f296dfe5a1cdd4575329","source":{"kind":"arxiv","id":"2503.08833","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.08833","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"arxiv_version","alias_value":"2503.08833v2","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.08833","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"pith_short_12","alias_value":"TEQNSQQTILAQ","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"pith_short_16","alias_value":"TEQNSQQTILAQDCQ2","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"pith_short_8","alias_value":"TEQNSQQT","created_at":"2026-05-20T00:02:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TEQNSQQTILAQDCQ2ERYJBK6ZNY","target":"record","payload":{"canonical_record":{"source":{"id":"2503.08833","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.TR","submitted_at":"2025-03-11T19:15:19Z","cross_cats_sorted":["q-fin.MF"],"title_canon_sha256":"bb4092512b78aa0584952538a4c0fcf72f76af9c1d2dd8d536a07ab5c386ca96","abstract_canon_sha256":"107c9cf905ea4626a1010037c2d531a126575782c7a5aa33e6506545e1bfe11d"},"schema_version":"1.0"},"canonical_sha256":"9920d9421342c1018a1a247090abd96e16f511903e61f296dfe5a1cdd4575329","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:04.134590Z","signature_b64":"IG0U9vQqziDxFzev31hHal3RDXifkOTEvK06lhsl4s24fpd65k9hGkpS3ewAgSpVnsY9Or1lrdujxx9ldrFuBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9920d9421342c1018a1a247090abd96e16f511903e61f296dfe5a1cdd4575329","last_reissued_at":"2026-05-20T00:02:04.133717Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:04.133717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.08833","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:02:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WAH5WhctR4I0pKw7L7uRi6NGdTfgoWj6CbODdb0rI5Q1oopMGDq76sCc5H7HtJN7dsrRIZjX4WNK/8KEAfSlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:02:45.453286Z"},"content_sha256":"f1b771f8c3bdd69515bd404be39753d7d84d093f8022b60d803d01e0cdb98b4f","schema_version":"1.0","event_id":"sha256:f1b771f8c3bdd69515bd404be39753d7d84d093f8022b60d803d01e0cdb98b4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TEQNSQQTILAQDCQ2ERYJBK6ZNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomization in Optimal Execution Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.MF"],"primary_cat":"q-fin.TR","authors_text":"Marcel Nutz, Steven Campbell","submitted_at":"2025-03-11T19:15:19Z","abstract_excerpt":"We study optimal execution in markets with transient price impact in a competitive setting with $N$ traders. Motivated by prior negative results on the existence of pure Nash equilibria, we consider randomized strategies for the traders and whether allowing such strategies can restore the existence of equilibria. We show that given a randomized strategy, there is a non-randomized strategy with strictly lower expected execution cost, and moreover this de-randomization can be achieved by a simple averaging procedure. As a consequence, Nash equilibria cannot contain randomized strategies, and non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.08833","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.08833/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":"2026-05-20T00:02:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xW0HW6pqFUCv9c9rFYmS2Od3TKjrmZc2rXBFLH7VgBn89YOYsYEBA3i9vEpG0i/4vB4PCW8z+vzVMK1kDIOxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:02:45.453766Z"},"content_sha256":"3956ec1efb521176fc17e31cd6a40444c3ef3e9133ac5fe8619ce5ebb9eb0fa3","schema_version":"1.0","event_id":"sha256:3956ec1efb521176fc17e31cd6a40444c3ef3e9133ac5fe8619ce5ebb9eb0fa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TEQNSQQTILAQDCQ2ERYJBK6ZNY/bundle.json","state_url":"https://pith.science/pith/TEQNSQQTILAQDCQ2ERYJBK6ZNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TEQNSQQTILAQDCQ2ERYJBK6ZNY/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":"2026-05-23T23:02:45Z","links":{"resolver":"https://pith.science/pith/TEQNSQQTILAQDCQ2ERYJBK6ZNY","bundle":"https://pith.science/pith/TEQNSQQTILAQDCQ2ERYJBK6ZNY/bundle.json","state":"https://pith.science/pith/TEQNSQQTILAQDCQ2ERYJBK6ZNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TEQNSQQTILAQDCQ2ERYJBK6ZNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TEQNSQQTILAQDCQ2ERYJBK6ZNY","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":"107c9cf905ea4626a1010037c2d531a126575782c7a5aa33e6506545e1bfe11d","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.TR","submitted_at":"2025-03-11T19:15:19Z","title_canon_sha256":"bb4092512b78aa0584952538a4c0fcf72f76af9c1d2dd8d536a07ab5c386ca96"},"schema_version":"1.0","source":{"id":"2503.08833","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.08833","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"arxiv_version","alias_value":"2503.08833v2","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.08833","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"pith_short_12","alias_value":"TEQNSQQTILAQ","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"pith_short_16","alias_value":"TEQNSQQTILAQDCQ2","created_at":"2026-05-20T00:02:04Z"},{"alias_kind":"pith_short_8","alias_value":"TEQNSQQT","created_at":"2026-05-20T00:02:04Z"}],"graph_snapshots":[{"event_id":"sha256:3956ec1efb521176fc17e31cd6a40444c3ef3e9133ac5fe8619ce5ebb9eb0fa3","target":"graph","created_at":"2026-05-20T00:02:04Z","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/2503.08833/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study optimal execution in markets with transient price impact in a competitive setting with $N$ traders. Motivated by prior negative results on the existence of pure Nash equilibria, we consider randomized strategies for the traders and whether allowing such strategies can restore the existence of equilibria. We show that given a randomized strategy, there is a non-randomized strategy with strictly lower expected execution cost, and moreover this de-randomization can be achieved by a simple averaging procedure. As a consequence, Nash equilibria cannot contain randomized strategies, and non","authors_text":"Marcel Nutz, Steven Campbell","cross_cats":["q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.TR","submitted_at":"2025-03-11T19:15:19Z","title":"Randomization in Optimal Execution Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.08833","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:f1b771f8c3bdd69515bd404be39753d7d84d093f8022b60d803d01e0cdb98b4f","target":"record","created_at":"2026-05-20T00:02:04Z","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":"107c9cf905ea4626a1010037c2d531a126575782c7a5aa33e6506545e1bfe11d","cross_cats_sorted":["q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.TR","submitted_at":"2025-03-11T19:15:19Z","title_canon_sha256":"bb4092512b78aa0584952538a4c0fcf72f76af9c1d2dd8d536a07ab5c386ca96"},"schema_version":"1.0","source":{"id":"2503.08833","kind":"arxiv","version":2}},"canonical_sha256":"9920d9421342c1018a1a247090abd96e16f511903e61f296dfe5a1cdd4575329","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9920d9421342c1018a1a247090abd96e16f511903e61f296dfe5a1cdd4575329","first_computed_at":"2026-05-20T00:02:04.133717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:04.133717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IG0U9vQqziDxFzev31hHal3RDXifkOTEvK06lhsl4s24fpd65k9hGkpS3ewAgSpVnsY9Or1lrdujxx9ldrFuBw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:04.134590Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.08833","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1b771f8c3bdd69515bd404be39753d7d84d093f8022b60d803d01e0cdb98b4f","sha256:3956ec1efb521176fc17e31cd6a40444c3ef3e9133ac5fe8619ce5ebb9eb0fa3"],"state_sha256":"dfd28e599fadb08d1244a70c93bbafa00879f38ab92e3c69d0ed40a4e47cea4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bjPn3WoAiZ84f/TTGmawtdAKdL8hRHYaYZArSn5NH3AsNtp4axKm9DKX6IZ2+54VxOoAQbBh8X+a1P2gXwYQCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T23:02:45.456344Z","bundle_sha256":"748cddd59f57ca9b5546607e2393492d56f8d4759f5dee2117d9493e34a56de8"}}