Pith Number

pith:SVMU7YBH

pith:2026:SVMU7YBHN4TUP2INM3XKFTTIVM

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Counterfactual Reasoning for Causal Responsibility Attribution in Probabilistic Multi-Agent Systems

Chunyan Mu, Muhammad Najib

Shapley values allocate responsibility fairly among agents in stochastic multi-agent games by quantifying retrospective counterfactual impact.

arxiv:2605.13077 v1 · 2026-05-13 · cs.MA · cs.AI

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Claims

C1strongest claim

we utilise the Shapley value and formally show that this method satisfies key desirable properties, including fairness and consistency.

C2weakest 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.

C3one 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.

References

54 extracted · 54 resolved · 0 Pith anchors

[1] Abarca, A.I.R., Broersen, J.M.: A stit logic of responsibility. In: AAMAS. pp. 1717–1719 (2022) 2022

[2] In: Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems 2007

[3] MIT Press (2008) 2008

[4] Baier, C., Funke, F., Majumdar, R.: A game-theoretic account of responsibility allocation. In: IJCAI. pp. 1773–1779. ijcai.org (2021) 2021

[5] 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 2021

Receipt and verification

First computed	2026-05-18T03:08:58.748332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95594fe0276f2747e90d66eea2ce68ab11d4b94d444ddc72967f977e288c49ad

Aliases

arxiv: 2605.13077 · arxiv_version: 2605.13077v1 · doi: 10.48550/arxiv.2605.13077 · pith_short_12: SVMU7YBHN4TU · pith_short_16: SVMU7YBHN4TUP2IN · pith_short_8: SVMU7YBH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SVMU7YBHN4TUP2INM3XKFTTIVM \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 95594fe0276f2747e90d66eea2ce68ab11d4b94d444ddc72967f977e288c49ad

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "7a8dff709cc1ef33874f81b1f1109dd62521a9c340855de01bac0c30287ca375",
    "cross_cats_sorted": [
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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.MA",
    "submitted_at": "2026-05-13T06:50:04Z",
    "title_canon_sha256": "6fb2c121b7d13d212beeed5c46220a737a5fd36cfd3896330074774d7e0d9381"
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}