{"paper":{"title":"Counterfactual Reasoning for Causal Responsibility Attribution in Probabilistic Multi-Agent Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Shapley values allocate responsibility fairly among agents in stochastic multi-agent games by quantifying retrospective counterfactual impact.","cross_cats":["cs.AI"],"primary_cat":"cs.MA","authors_text":"Chunyan Mu, Muhammad Najib","submitted_at":"2026-05-13T06:50:04Z","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"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we utilise the Shapley value and formally show that this method satisfies key desirable properties, including fairness and consistency.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Shapley values allocate responsibility fairly among agents in stochastic multi-agent games by quantifying retrospective counterfactual impact.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7aef6d4466647788f603ee975771da4aced80cc1c5901dbf7061cfeb5799fa3c"},"source":{"id":"2605.13077","kind":"arxiv","version":1},"verdict":{"id":"c76b75ca-669f-43bd-8800-d5c90bf3a231","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T02:10:25.733614Z","strongest_claim":"we utilise the Shapley value and formally show that this method satisfies key desirable properties, including fairness and consistency.","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","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.","pith_extraction_headline":"Shapley values allocate responsibility fairly among agents in stochastic multi-agent games by quantifying retrospective counterfactual impact."},"references":{"count":54,"sample":[{"doi":"","year":2022,"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","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"In: Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems","work_id":"e595eca4-a1f5-4743-8a52-1c915b42d0a5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"MIT Press (2008)","work_id":"8c09b0b7-1da3-48a8-a94b-962ecf247d27","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"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","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"Baier, C., Funke, F., Majumdar, R.: Responsibility attribution in parameterized markovian models. In: AAAI. pp. 11734–11743. 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