{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6YIEZMYCDP4AXLZXII7L4UNUQB","short_pith_number":"pith:6YIEZMYC","canonical_record":{"source":{"id":"1310.7654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-10-29T00:57:02Z","cross_cats_sorted":[],"title_canon_sha256":"2dc2ad7b0305d56c612e6caaac1e344eae61385d8704c30b1e9dc6b95cd606d3","abstract_canon_sha256":"72395bc22168039b89281a49d8c3870c0e1a6486f8a96db8d7b138af969797e3"},"schema_version":"1.0"},"canonical_sha256":"f6104cb3021bf80baf37423ebe51b4806af30825ef10f466e7eff09c5f9e4eca","source":{"kind":"arxiv","id":"1310.7654","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7654","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7654v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7654","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"6YIEZMYCDP4A","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6YIEZMYCDP4AXLZX","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6YIEZMYC","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6YIEZMYCDP4AXLZXII7L4UNUQB","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-10-29T00:57:02Z","cross_cats_sorted":[],"title_canon_sha256":"2dc2ad7b0305d56c612e6caaac1e344eae61385d8704c30b1e9dc6b95cd606d3","abstract_canon_sha256":"72395bc22168039b89281a49d8c3870c0e1a6486f8a96db8d7b138af969797e3"},"schema_version":"1.0"},"canonical_sha256":"f6104cb3021bf80baf37423ebe51b4806af30825ef10f466e7eff09c5f9e4eca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:48.591687Z","signature_b64":"PYbVzZQcolwJFlaq3/zMhUSy7imDUqfkDky9DZd8s/QQAXxXKO7Q+YGW5qWesX/Gqd/u2xNL/RK8PXhTZm3dCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6104cb3021bf80baf37423ebe51b4806af30825ef10f466e7eff09c5f9e4eca","last_reissued_at":"2026-05-18T02:39:48.591210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:48.591210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7654","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":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7in0JIgFQqPKvp+4uzfLoGEhOzQcSVZ/j42qxP/Mp27+4BBjj7G9N6RRVOkILkIJm1lWpkZvUXLjlzp7k+HQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:22:04.283111Z"},"content_sha256":"fefbdc18504e32d2ed3c039290551664ef077aaee007e7c192b389c9e43d7989","schema_version":"1.0","event_id":"sha256:fefbdc18504e32d2ed3c039290551664ef077aaee007e7c192b389c9e43d7989"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6YIEZMYCDP4AXLZXII7L4UNUQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Empirical Distribution of Equilibrium Play and Its Testing Application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Ron Peretz, Siddharth Barman, Yakov Babichenko","submitted_at":"2013-10-29T00:57:02Z","abstract_excerpt":"We show that in any $n$-player $m$-action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated and coarse correlated. For each one of them we obtain upper and lower bounds on the number of samples required for the empirical distribution over the sampled action profiles to form an approximate equilibrium with probability close to one.\n  These bounds imply that using a small number of samples we can test whether or not players are playing according to an approximate equili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7654","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":"2026-05-18T02:39:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IGP7JjPeg4ylVgfdFbm0ZafRthUtb0GN5JuHY8oncu4wdi18QaHUOvGi0WuiYSaxMnlrvRE+s5dlQfMXfHWuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:22:04.283727Z"},"content_sha256":"8788828c0146e2328cd6dbc6ed96d26e9365e0af83265ca4dc0572753038f993","schema_version":"1.0","event_id":"sha256:8788828c0146e2328cd6dbc6ed96d26e9365e0af83265ca4dc0572753038f993"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YIEZMYCDP4AXLZXII7L4UNUQB/bundle.json","state_url":"https://pith.science/pith/6YIEZMYCDP4AXLZXII7L4UNUQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YIEZMYCDP4AXLZXII7L4UNUQB/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":"2026-06-09T02:22:04Z","links":{"resolver":"https://pith.science/pith/6YIEZMYCDP4AXLZXII7L4UNUQB","bundle":"https://pith.science/pith/6YIEZMYCDP4AXLZXII7L4UNUQB/bundle.json","state":"https://pith.science/pith/6YIEZMYCDP4AXLZXII7L4UNUQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YIEZMYCDP4AXLZXII7L4UNUQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6YIEZMYCDP4AXLZXII7L4UNUQB","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":"72395bc22168039b89281a49d8c3870c0e1a6486f8a96db8d7b138af969797e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-10-29T00:57:02Z","title_canon_sha256":"2dc2ad7b0305d56c612e6caaac1e344eae61385d8704c30b1e9dc6b95cd606d3"},"schema_version":"1.0","source":{"id":"1310.7654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7654","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7654v2","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7654","created_at":"2026-05-18T02:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"6YIEZMYCDP4A","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6YIEZMYCDP4AXLZX","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6YIEZMYC","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:8788828c0146e2328cd6dbc6ed96d26e9365e0af83265ca4dc0572753038f993","target":"graph","created_at":"2026-05-18T02:39:48Z","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 show that in any $n$-player $m$-action normal-form game, we can obtain an approximate equilibrium by sampling any mixed-action equilibrium a small number of times. We study three types of equilibria: Nash, correlated and coarse correlated. For each one of them we obtain upper and lower bounds on the number of samples required for the empirical distribution over the sampled action profiles to form an approximate equilibrium with probability close to one.\n  These bounds imply that using a small number of samples we can test whether or not players are playing according to an approximate equili","authors_text":"Ron Peretz, Siddharth Barman, Yakov Babichenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-10-29T00:57:02Z","title":"Empirical Distribution of Equilibrium Play and Its Testing Application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7654","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:fefbdc18504e32d2ed3c039290551664ef077aaee007e7c192b389c9e43d7989","target":"record","created_at":"2026-05-18T02:39:48Z","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":"72395bc22168039b89281a49d8c3870c0e1a6486f8a96db8d7b138af969797e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-10-29T00:57:02Z","title_canon_sha256":"2dc2ad7b0305d56c612e6caaac1e344eae61385d8704c30b1e9dc6b95cd606d3"},"schema_version":"1.0","source":{"id":"1310.7654","kind":"arxiv","version":2}},"canonical_sha256":"f6104cb3021bf80baf37423ebe51b4806af30825ef10f466e7eff09c5f9e4eca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6104cb3021bf80baf37423ebe51b4806af30825ef10f466e7eff09c5f9e4eca","first_computed_at":"2026-05-18T02:39:48.591210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:48.591210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PYbVzZQcolwJFlaq3/zMhUSy7imDUqfkDky9DZd8s/QQAXxXKO7Q+YGW5qWesX/Gqd/u2xNL/RK8PXhTZm3dCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:48.591687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fefbdc18504e32d2ed3c039290551664ef077aaee007e7c192b389c9e43d7989","sha256:8788828c0146e2328cd6dbc6ed96d26e9365e0af83265ca4dc0572753038f993"],"state_sha256":"399f6a3dffebab3cbb2bb5ec2dbc7d631b60064dbc7500487f3b5f1045304c45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F0wVKZcGdbB6cpPsCNBU6bXi/G21+twr0ztdyxiIXXoS58V33nY8/4yVfiAxq0bfvkW8n3o3ggEnVIS+VTLTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:22:04.287211Z","bundle_sha256":"f856508e640ac6f2702e977ba97a1c441df26b5dfd7d4a80b4610489d5e6dc5a"}}