{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KV6PEWWUMCR7HFKVKHFLU6SQ4B","short_pith_number":"pith:KV6PEWWU","canonical_record":{"source":{"id":"1308.6255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-08-28T19:16:05Z","cross_cats_sorted":[],"title_canon_sha256":"f013de9771e8f59ecb02681b97395b99da2e7077c4a5a5655373292f27ae2365","abstract_canon_sha256":"a23d0c3ec717d69959c40b23bc87770639de648f261db8a85f3e787ea2521118"},"schema_version":"1.0"},"canonical_sha256":"557cf25ad460a3f3955551caba7a50e055bbdc741a34337b5627d31032ee5f11","source":{"kind":"arxiv","id":"1308.6255","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6255","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6255v1","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6255","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"KV6PEWWUMCR7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KV6PEWWUMCR7HFKV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KV6PEWWU","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KV6PEWWUMCR7HFKVKHFLU6SQ4B","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-08-28T19:16:05Z","cross_cats_sorted":[],"title_canon_sha256":"f013de9771e8f59ecb02681b97395b99da2e7077c4a5a5655373292f27ae2365","abstract_canon_sha256":"a23d0c3ec717d69959c40b23bc87770639de648f261db8a85f3e787ea2521118"},"schema_version":"1.0"},"canonical_sha256":"557cf25ad460a3f3955551caba7a50e055bbdc741a34337b5627d31032ee5f11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:48.725442Z","signature_b64":"4dJpLWeYQMug0VYDLyaj/sNBck/vPPW7eb/CV3Lr+k9lMwa0OpnYOk4J5Ewz5uGrs3qYamB2U232JN3SvmbRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"557cf25ad460a3f3955551caba7a50e055bbdc741a34337b5627d31032ee5f11","last_reissued_at":"2026-05-18T03:14:48.724756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:48.724756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6255","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":"2026-05-18T03:14:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//nM1RCgyPYZGPwFm32qQG7gvwBa9elsdXb/d+hhVuumdUguDrbbpybvoCAvrVba3srD76c6jVOiNDlrM0rGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:07:18.231818Z"},"content_sha256":"93569692874913a3da095a80fb2d56c582ac16f669de77f99b461950b33be9a3","schema_version":"1.0","event_id":"sha256:93569692874913a3da095a80fb2d56c582ac16f669de77f99b461950b33be9a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KV6PEWWUMCR7HFKVKHFLU6SQ4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Shapley Axiomatization for Values in Partition Function Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Michael Wooldridge, Oskar Skibski, Tomasz P. Michalak","submitted_at":"2013-08-28T19:16:05Z","abstract_excerpt":"One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player's marginal contribution - a central notion to the Shapley value - be defined in a variety of ways, but it is also not obvious which axiomatization should be used. Consequently, a number of authors extended the Shapley value using complex and often unintuitive axiomatizations. Furthermore, no algorithm to approximate any extension of the Shapley value to partition-function games has been propose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6255","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":"2026-05-18T03:14:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRILueN6ba4YAIKZ6274ggIYsvhmNcrC6iS5924Fzb8q8PP5oX+/DCxI8U8eFdX9rKsHcoU8bpivQFotIH6bAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:07:18.232522Z"},"content_sha256":"c321b06faee47a331a3f01ec80743b78926db67d04314c7249c8ca6dd26fe523","schema_version":"1.0","event_id":"sha256:c321b06faee47a331a3f01ec80743b78926db67d04314c7249c8ca6dd26fe523"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KV6PEWWUMCR7HFKVKHFLU6SQ4B/bundle.json","state_url":"https://pith.science/pith/KV6PEWWUMCR7HFKVKHFLU6SQ4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KV6PEWWUMCR7HFKVKHFLU6SQ4B/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":"2026-06-09T10:07:18Z","links":{"resolver":"https://pith.science/pith/KV6PEWWUMCR7HFKVKHFLU6SQ4B","bundle":"https://pith.science/pith/KV6PEWWUMCR7HFKVKHFLU6SQ4B/bundle.json","state":"https://pith.science/pith/KV6PEWWUMCR7HFKVKHFLU6SQ4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KV6PEWWUMCR7HFKVKHFLU6SQ4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KV6PEWWUMCR7HFKVKHFLU6SQ4B","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":"a23d0c3ec717d69959c40b23bc87770639de648f261db8a85f3e787ea2521118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-08-28T19:16:05Z","title_canon_sha256":"f013de9771e8f59ecb02681b97395b99da2e7077c4a5a5655373292f27ae2365"},"schema_version":"1.0","source":{"id":"1308.6255","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6255","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6255v1","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6255","created_at":"2026-05-18T03:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"KV6PEWWUMCR7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KV6PEWWUMCR7HFKV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KV6PEWWU","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:c321b06faee47a331a3f01ec80743b78926db67d04314c7249c8ca6dd26fe523","target":"graph","created_at":"2026-05-18T03:14:48Z","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":"One of the long-debated issues in coalitional game theory is how to extend the Shapley value to games with externalities (partition-function games). When externalities are present, not only can a player's marginal contribution - a central notion to the Shapley value - be defined in a variety of ways, but it is also not obvious which axiomatization should be used. Consequently, a number of authors extended the Shapley value using complex and often unintuitive axiomatizations. Furthermore, no algorithm to approximate any extension of the Shapley value to partition-function games has been propose","authors_text":"Michael Wooldridge, Oskar Skibski, Tomasz P. Michalak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-08-28T19:16:05Z","title":"The Shapley Axiomatization for Values in Partition Function Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6255","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":"sha256:93569692874913a3da095a80fb2d56c582ac16f669de77f99b461950b33be9a3","target":"record","created_at":"2026-05-18T03:14:48Z","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":"a23d0c3ec717d69959c40b23bc87770639de648f261db8a85f3e787ea2521118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-08-28T19:16:05Z","title_canon_sha256":"f013de9771e8f59ecb02681b97395b99da2e7077c4a5a5655373292f27ae2365"},"schema_version":"1.0","source":{"id":"1308.6255","kind":"arxiv","version":1}},"canonical_sha256":"557cf25ad460a3f3955551caba7a50e055bbdc741a34337b5627d31032ee5f11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"557cf25ad460a3f3955551caba7a50e055bbdc741a34337b5627d31032ee5f11","first_computed_at":"2026-05-18T03:14:48.724756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:48.724756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4dJpLWeYQMug0VYDLyaj/sNBck/vPPW7eb/CV3Lr+k9lMwa0OpnYOk4J5Ewz5uGrs3qYamB2U232JN3SvmbRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:48.725442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93569692874913a3da095a80fb2d56c582ac16f669de77f99b461950b33be9a3","sha256:c321b06faee47a331a3f01ec80743b78926db67d04314c7249c8ca6dd26fe523"],"state_sha256":"a171f55c069ca23cac4b718f7083543cdc95fb7d7120b1e802f1a6d1ae5454ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"idff5lURV6/ya0fMTl7kh+GT6NQLABOH3YWqR1eDfYEqfcWYEOZUlviRb5aue/hreyre3+xazF8/lc74ZBimBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:07:18.236810Z","bundle_sha256":"123556cbe080c3348143decc2e7e798d4593cd7cb1fafcfd67b3bc17c5122328"}}