{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4VLFDC2IBA4YRKCMVY272GC35S","short_pith_number":"pith:4VLFDC2I","canonical_record":{"source":{"id":"1103.1040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-03-05T10:37:48Z","cross_cats_sorted":[],"title_canon_sha256":"528a7d42d0d2053d8e5bc02f3c39e6022bbcd30e94726ee8c8d63e10267f947f","abstract_canon_sha256":"a853f57fa609a0bf44b4e633cf3cccd70619ca54f21c3b1222b17f4b11b86786"},"schema_version":"1.0"},"canonical_sha256":"e556518b48083988a84cae35fd185becbce598f38fb779f7a3cd1ecf4bcaf024","source":{"kind":"arxiv","id":"1103.1040","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1040","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1040v2","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1040","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"4VLFDC2IBA4Y","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4VLFDC2IBA4YRKCM","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4VLFDC2I","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4VLFDC2IBA4YRKCMVY272GC35S","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-03-05T10:37:48Z","cross_cats_sorted":[],"title_canon_sha256":"528a7d42d0d2053d8e5bc02f3c39e6022bbcd30e94726ee8c8d63e10267f947f","abstract_canon_sha256":"a853f57fa609a0bf44b4e633cf3cccd70619ca54f21c3b1222b17f4b11b86786"},"schema_version":"1.0"},"canonical_sha256":"e556518b48083988a84cae35fd185becbce598f38fb779f7a3cd1ecf4bcaf024","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:22.521276Z","signature_b64":"Cr5tFN9agLdZ62YAzdT99t/n7Dy0iYfSgQsnBQiGp4zprkMCzJd7byDb0SHb4oLOeAP1OtHVhy1U+Zm6ZRpbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e556518b48083988a84cae35fd185becbce598f38fb779f7a3cd1ecf4bcaf024","last_reissued_at":"2026-05-18T04:26:22.520688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:22.520688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1040","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":"2026-05-18T04:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qzba6Yb3oOLrq7qColWOpTJbtoMQip2K1KwyLQFCZeoHvpJruX0wI0pJ66oBXyBxrUZIvVvs2Jj8MVMNNB5ECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:15:41.111642Z"},"content_sha256":"68993c96126f0ec12aa082c94b7cc1c3c316641dab42946e6eb1c9022fe18ed1","schema_version":"1.0","event_id":"sha256:68993c96126f0ec12aa082c94b7cc1c3c316641dab42946e6eb1c9022fe18ed1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4VLFDC2IBA4YRKCMVY272GC35S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Approximation Performance of Fictitious Play in Finite Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Carmine Ventre, Paul W. Goldberg, Rahul Savani, Troels Bjerre Sorensen","submitted_at":"2011-03-05T10:37:48Z","abstract_excerpt":"We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play fails to find a solution having an additive approximation guarantee significantly better than 1/2. Our construction shows that for n times n games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity 1/2 - O(1/n^(1-delta)) for arbitrarily small delta. We also show an essential"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1040","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WhdaLyhZiC27JBTbRO+g1ceqVqYDTuKzKUMVJYbo2IeDWhj8woy8C8TRHeLkdXODWgTVjnBW1IGT3XwmEgf6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:15:41.112347Z"},"content_sha256":"b082cb5031a05ec980a306d1c51aa58f48ea462a9c87bfe83dda25fbea446d93","schema_version":"1.0","event_id":"sha256:b082cb5031a05ec980a306d1c51aa58f48ea462a9c87bfe83dda25fbea446d93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VLFDC2IBA4YRKCMVY272GC35S/bundle.json","state_url":"https://pith.science/pith/4VLFDC2IBA4YRKCMVY272GC35S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VLFDC2IBA4YRKCMVY272GC35S/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":"2026-05-25T22:15:41Z","links":{"resolver":"https://pith.science/pith/4VLFDC2IBA4YRKCMVY272GC35S","bundle":"https://pith.science/pith/4VLFDC2IBA4YRKCMVY272GC35S/bundle.json","state":"https://pith.science/pith/4VLFDC2IBA4YRKCMVY272GC35S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VLFDC2IBA4YRKCMVY272GC35S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4VLFDC2IBA4YRKCMVY272GC35S","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":"a853f57fa609a0bf44b4e633cf3cccd70619ca54f21c3b1222b17f4b11b86786","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-03-05T10:37:48Z","title_canon_sha256":"528a7d42d0d2053d8e5bc02f3c39e6022bbcd30e94726ee8c8d63e10267f947f"},"schema_version":"1.0","source":{"id":"1103.1040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1040","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1040v2","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1040","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"4VLFDC2IBA4Y","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4VLFDC2IBA4YRKCM","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4VLFDC2I","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:b082cb5031a05ec980a306d1c51aa58f48ea462a9c87bfe83dda25fbea446d93","target":"graph","created_at":"2026-05-18T04:26:22Z","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":"We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play fails to find a solution having an additive approximation guarantee significantly better than 1/2. Our construction shows that for n times n games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity 1/2 - O(1/n^(1-delta)) for arbitrarily small delta. We also show an essential","authors_text":"Carmine Ventre, Paul W. Goldberg, Rahul Savani, Troels Bjerre Sorensen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-03-05T10:37:48Z","title":"On the Approximation Performance of Fictitious Play in Finite Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1040","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":"sha256:68993c96126f0ec12aa082c94b7cc1c3c316641dab42946e6eb1c9022fe18ed1","target":"record","created_at":"2026-05-18T04:26:22Z","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":"a853f57fa609a0bf44b4e633cf3cccd70619ca54f21c3b1222b17f4b11b86786","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-03-05T10:37:48Z","title_canon_sha256":"528a7d42d0d2053d8e5bc02f3c39e6022bbcd30e94726ee8c8d63e10267f947f"},"schema_version":"1.0","source":{"id":"1103.1040","kind":"arxiv","version":2}},"canonical_sha256":"e556518b48083988a84cae35fd185becbce598f38fb779f7a3cd1ecf4bcaf024","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e556518b48083988a84cae35fd185becbce598f38fb779f7a3cd1ecf4bcaf024","first_computed_at":"2026-05-18T04:26:22.520688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:22.520688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cr5tFN9agLdZ62YAzdT99t/n7Dy0iYfSgQsnBQiGp4zprkMCzJd7byDb0SHb4oLOeAP1OtHVhy1U+Zm6ZRpbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:22.521276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68993c96126f0ec12aa082c94b7cc1c3c316641dab42946e6eb1c9022fe18ed1","sha256:b082cb5031a05ec980a306d1c51aa58f48ea462a9c87bfe83dda25fbea446d93"],"state_sha256":"71d6722f691dd92d9855be611d3efc785353425178a4037b25d5297ebdb67588"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"prasEXFkqW5WzUQpbJmSoN3zE1MYXsR6Dbp6Nd0l8hhxRDj22vmHgdgel1b8+jC/Z7arojujcC75ZQVX9HdBAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:15:41.116203Z","bundle_sha256":"cbe9005418e286ee27e055aa097c84db2c1d1101faf0b7d7335ee936f1a3ffe5"}}