{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:X3Z27EPZOJOSWZ5JVTRBS7TCKD","short_pith_number":"pith:X3Z27EPZ","canonical_record":{"source":{"id":"1307.2051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-08T11:55:23Z","cross_cats_sorted":[],"title_canon_sha256":"7a2f6232a522381a77a7e76eb8ad1c6dfd985b5c42935915174549b69ae2f593","abstract_canon_sha256":"c77db157cfd11e8611f16d27ca60f5ddaebf0dc9fdcaba3539019b93a7b145e4"},"schema_version":"1.0"},"canonical_sha256":"bef3af91f9725d2b67a9ace2197e6250cc0f0b6c1b4d9b3c1a3ab406fa35075b","source":{"kind":"arxiv","id":"1307.2051","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2051","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2051v1","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2051","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"X3Z27EPZOJOS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"X3Z27EPZOJOSWZ5J","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"X3Z27EPZ","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:X3Z27EPZOJOSWZ5JVTRBS7TCKD","target":"record","payload":{"canonical_record":{"source":{"id":"1307.2051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-08T11:55:23Z","cross_cats_sorted":[],"title_canon_sha256":"7a2f6232a522381a77a7e76eb8ad1c6dfd985b5c42935915174549b69ae2f593","abstract_canon_sha256":"c77db157cfd11e8611f16d27ca60f5ddaebf0dc9fdcaba3539019b93a7b145e4"},"schema_version":"1.0"},"canonical_sha256":"bef3af91f9725d2b67a9ace2197e6250cc0f0b6c1b4d9b3c1a3ab406fa35075b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:02.623707Z","signature_b64":"YfYXhJHc1oU9fj7VwyOuAbpaReAuO40MPydsbLFGNMQhZA8o5O2OkQ2XOA5uGhawiMG2hJFvyOfslvVsrQlRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bef3af91f9725d2b67a9ace2197e6250cc0f0b6c1b4d9b3c1a3ab406fa35075b","last_reissued_at":"2026-05-18T03:19:02.623043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:02.623043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.2051","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":"2026-05-18T03:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/nyJaHVWtlXk0DSaCatsbEBdINfGglcQaRTYEAh5+XifBKmA7YJOCtFvFRFdqDTppYgdChh+hj+HR76exZVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:19:34.647428Z"},"content_sha256":"62e079ce4c3df850d061a12335731adda3f1cb4dad15425cf44b4908e49c5a88","schema_version":"1.0","event_id":"sha256:62e079ce4c3df850d061a12335731adda3f1cb4dad15425cf44b4908e49c5a88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:X3Z27EPZOJOSWZ5JVTRBS7TCKD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The benefit of law-making power","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Anshul Gupta, Sven Schewe","submitted_at":"2013-07-08T11:55:23Z","abstract_excerpt":"We study optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no player has an incentive to deviate from her strategy. We argue that a player with the power to define an equilibrium is in a position, where she should not be interested in the symmetry of a Nash equilibrium, and ignore the question of whether or not her outcome can be improved if the other strategies are fixed. That is, she would only have to make sure that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2051","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":""},"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":"2026-05-18T03:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qhh9u1I4ceT6mwnZQlmca42xHjpgQy+jWO2asZOXOHT8oCHtJ/2JPdNIqAJLugqX44b25q5wPzwNQiQzDhkYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:19:34.647774Z"},"content_sha256":"363e36de6e2a1a2b0c82fabeffab2a65724c76c34843be71e6dd0e1cd4fb777c","schema_version":"1.0","event_id":"sha256:363e36de6e2a1a2b0c82fabeffab2a65724c76c34843be71e6dd0e1cd4fb777c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X3Z27EPZOJOSWZ5JVTRBS7TCKD/bundle.json","state_url":"https://pith.science/pith/X3Z27EPZOJOSWZ5JVTRBS7TCKD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X3Z27EPZOJOSWZ5JVTRBS7TCKD/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":"2026-06-02T22:19:34Z","links":{"resolver":"https://pith.science/pith/X3Z27EPZOJOSWZ5JVTRBS7TCKD","bundle":"https://pith.science/pith/X3Z27EPZOJOSWZ5JVTRBS7TCKD/bundle.json","state":"https://pith.science/pith/X3Z27EPZOJOSWZ5JVTRBS7TCKD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X3Z27EPZOJOSWZ5JVTRBS7TCKD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:X3Z27EPZOJOSWZ5JVTRBS7TCKD","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":"c77db157cfd11e8611f16d27ca60f5ddaebf0dc9fdcaba3539019b93a7b145e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-08T11:55:23Z","title_canon_sha256":"7a2f6232a522381a77a7e76eb8ad1c6dfd985b5c42935915174549b69ae2f593"},"schema_version":"1.0","source":{"id":"1307.2051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2051","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2051v1","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2051","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"X3Z27EPZOJOS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"X3Z27EPZOJOSWZ5J","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"X3Z27EPZ","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:363e36de6e2a1a2b0c82fabeffab2a65724c76c34843be71e6dd0e1cd4fb777c","target":"graph","created_at":"2026-05-18T03:19:02Z","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 optimal equilibria in multi-player games. An equilibrium is optimal for a player, if her payoff is maximal. A tempting approach to solving this problem is to seek optimal Nash equilibria, the standard form of equilibria where no player has an incentive to deviate from her strategy. We argue that a player with the power to define an equilibrium is in a position, where she should not be interested in the symmetry of a Nash equilibrium, and ignore the question of whether or not her outcome can be improved if the other strategies are fixed. That is, she would only have to make sure that t","authors_text":"Anshul Gupta, Sven Schewe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-08T11:55:23Z","title":"The benefit of law-making power"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2051","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":"sha256:62e079ce4c3df850d061a12335731adda3f1cb4dad15425cf44b4908e49c5a88","target":"record","created_at":"2026-05-18T03:19:02Z","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":"c77db157cfd11e8611f16d27ca60f5ddaebf0dc9fdcaba3539019b93a7b145e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-07-08T11:55:23Z","title_canon_sha256":"7a2f6232a522381a77a7e76eb8ad1c6dfd985b5c42935915174549b69ae2f593"},"schema_version":"1.0","source":{"id":"1307.2051","kind":"arxiv","version":1}},"canonical_sha256":"bef3af91f9725d2b67a9ace2197e6250cc0f0b6c1b4d9b3c1a3ab406fa35075b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bef3af91f9725d2b67a9ace2197e6250cc0f0b6c1b4d9b3c1a3ab406fa35075b","first_computed_at":"2026-05-18T03:19:02.623043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:02.623043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YfYXhJHc1oU9fj7VwyOuAbpaReAuO40MPydsbLFGNMQhZA8o5O2OkQ2XOA5uGhawiMG2hJFvyOfslvVsrQlRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:02.623707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62e079ce4c3df850d061a12335731adda3f1cb4dad15425cf44b4908e49c5a88","sha256:363e36de6e2a1a2b0c82fabeffab2a65724c76c34843be71e6dd0e1cd4fb777c"],"state_sha256":"efcdf4a137b7a18d4fbb781b35b9cdb15af68d98e7d9a5e8349526a154f028ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zSbBUW0IK6f9wWM3+Y+vtsRH3sTDyrr705SVuoG2nty0Usro1dlHGG0/SeR+Yb/p5LC9BLYoK5tihTznGR+TDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:19:34.649733Z","bundle_sha256":"4dbe690a4cd4b71fc77a601ac508ad91195ab1869edbcef179dc4f34ce7f0425"}}