{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SVMU7YBHN4TUP2INM3XKFTTIVM","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":"7a8dff709cc1ef33874f81b1f1109dd62521a9c340855de01bac0c30287ca375","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-05-13T06:50:04Z","title_canon_sha256":"6fb2c121b7d13d212beeed5c46220a737a5fd36cfd3896330074774d7e0d9381"},"schema_version":"1.0","source":{"id":"2605.13077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13077","created_at":"2026-05-18T03:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13077v1","created_at":"2026-05-18T03:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13077","created_at":"2026-05-18T03:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"SVMU7YBHN4TU","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"SVMU7YBHN4TUP2IN","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"SVMU7YBH","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:34b39b0d7b385ff019f931b1ad37d0e47e625e53bc1c2aad3657d9f004b71418","target":"graph","created_at":"2026-05-18T03:08:58Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"we utilise the Shapley value and formally show that this method satisfies key desirable properties, including fairness and consistency."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That responsibility attribution in probabilistic multi-agent systems can be fully captured by retrospective counterfactuals within a concurrent stochastic game model without needing domain-specific adjustments beyond the Shapley value."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Defines retrospective counterfactual responsibility in concurrent stochastic multi-player games, allocates it via Shapley values satisfying fairness and consistency, and uses Nash equilibria for stable responsibility-reward tradeoffs."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Shapley values allocate responsibility fairly among agents in stochastic multi-agent games by quantifying retrospective counterfactual impact."}],"snapshot_sha256":"7aef6d4466647788f603ee975771da4aced80cc1c5901dbf7061cfeb5799fa3c"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Responsibility allocation -- determining the extent to which agents are accountable for outcomes -- is a fundamental challenge in the design and analysis of multi-agent systems. In this work, we model such systems as concurrent stochastic multi-player games and introduce a notion of retrospective (backward) counterfactual responsibility, which quantifies an agent's accountability for outcomes resulting from a given strategy profile. To allocate responsibility among agents, we utilise the Shapley value and formally show that this method satisfies key desirable properties, including fairness and","authors_text":"Chunyan Mu, Muhammad Najib","cross_cats":["cs.AI"],"headline":"Shapley values allocate responsibility fairly among agents in stochastic multi-agent games by quantifying retrospective counterfactual impact.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-05-13T06:50:04Z","title":"Counterfactual Reasoning for Causal Responsibility Attribution in Probabilistic Multi-Agent Systems"},"references":{"count":54,"internal_anchors":0,"resolved_work":54,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Abarca, A.I.R., Broersen, J.M.: A stit logic of responsibility. In: AAMAS. pp. 1717–1719 (2022)","work_id":"0a92623c-783a-4252-84b4-d02df2aece79","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"In: Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems","work_id":"e595eca4-a1f5-4743-8a52-1c915b42d0a5","year":2007},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"MIT Press (2008)","work_id":"8c09b0b7-1da3-48a8-a94b-962ecf247d27","year":2008},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Baier, C., Funke, F., Majumdar, R.: A game-theoretic account of responsibility allocation. In: IJCAI. pp. 1773–1779. ijcai.org (2021)","work_id":"d051a9bc-0f20-4295-99b4-79ed942b28b2","year":2021},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Baier, C., Funke, F., Majumdar, R.: Responsibility attribution in parameterized markovian models. In: AAAI. pp. 11734–11743. AAAI Press (2021) Counterfactual Reasoning for CR Attribution in Probabilis","work_id":"8171b9e3-2300-45f8-a7f0-9f2965c4b6c5","year":2021}],"snapshot_sha256":"d28a0ee79b2ac93914ca637f68bbc0788fe835528409d85593f2926d93166262"},"source":{"id":"2605.13077","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T02:10:25.733614Z","id":"c76b75ca-669f-43bd-8800-d5c90bf3a231","model_set":{"reader":"grok-4.3"},"one_line_summary":"Defines retrospective counterfactual responsibility in concurrent stochastic multi-player games, allocates it via Shapley values satisfying fairness and consistency, and uses Nash equilibria for stable responsibility-reward tradeoffs.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Shapley values allocate responsibility fairly among agents in stochastic multi-agent games by quantifying retrospective counterfactual impact.","strongest_claim":"we utilise the Shapley value and formally show that this method satisfies key desirable properties, including fairness and consistency.","weakest_assumption":"That responsibility attribution in probabilistic multi-agent systems can be fully captured by retrospective counterfactuals within a concurrent stochastic game model without needing domain-specific adjustments beyond the Shapley value."}},"verdict_id":"c76b75ca-669f-43bd-8800-d5c90bf3a231"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:83534927366905d1dcc556bcbda9cfe9321d52c77105d13f9b216da23d855b2e","target":"record","created_at":"2026-05-18T03:08:58Z","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":"7a8dff709cc1ef33874f81b1f1109dd62521a9c340855de01bac0c30287ca375","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2026-05-13T06:50:04Z","title_canon_sha256":"6fb2c121b7d13d212beeed5c46220a737a5fd36cfd3896330074774d7e0d9381"},"schema_version":"1.0","source":{"id":"2605.13077","kind":"arxiv","version":1}},"canonical_sha256":"95594fe0276f2747e90d66eea2ce68ab11d4b94d444ddc72967f977e288c49ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95594fe0276f2747e90d66eea2ce68ab11d4b94d444ddc72967f977e288c49ad","first_computed_at":"2026-05-18T03:08:58.748332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:58.748332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y0P9poGhp4jc/Gv1NWga+Ri3qIFVTERBuaMtg03zDMtCTUbg9ThbCqLVS/1csj5Fq3wt0Y5HnMZ3ZbYeIIKCCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:58.748871Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83534927366905d1dcc556bcbda9cfe9321d52c77105d13f9b216da23d855b2e","sha256:34b39b0d7b385ff019f931b1ad37d0e47e625e53bc1c2aad3657d9f004b71418"],"state_sha256":"9169167e464f82da01e4995e38096aaf8649f9f5005e6ffdae79f4e65049b1f6"}