Pith Number

pith:TB53WWDI

pith:2026:TB53WWDIMHXDOFWAA75QP3P2VN

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Efficient liability assignment under shock propagation

Alexandros Rigos, Jens Gudmundsson, Jens Leth Hougaard, Kohmei Makihara

Proportional liability rules with network-only weights induce agents to select paths minimizing total cascade losses.

arxiv:2605.14485 v1 · 2026-05-14 · econ.TH

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Our main axiomatic result characterizes a family of rules, which set each agent's liability to be proportional to the system's total realized losses with agent weights depending only on the network structure.

C2weakest assumption

The sequential-move game induced by the liability rule leads agents to select efficient paths; this relies on the assumption that the cascade mechanism and loss structure are exactly as modeled and that agents act to minimize their own expected liability under the proportional rule.

C3one line summary

A family of liability rules sets payments proportional to total realized losses with network-structure weights that implement efficient path selection in sequential shock games, coinciding with the Shapley value of a path-counting cooperative game and computable in polynomial time.

References

46 extracted · 46 resolved · 0 Pith anchors

[1] Anshelevich, E. and Dasgupta, A. and Kleinberg, J. and Tardos, E. and Wexler, T. and Roughgarden, T. , title =. SIAM Journal on Computing , year =

[2] Bakshi, N and Kleindorfer, P. , title =. Production and Operations Management , year =

[3] Bakshi, N. and Mohan, S. , title =. Manufactoring & Service Operations Management , year =

[4] Salvador Barberà and Dolors Berga and Bernardo Moreno , journal =

[5] Jackson , title = 1995

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:06.502718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

987bbb586861ee3716c007fb07edfaab5653147975de40c8050fb7b63f0bac07

Aliases

arxiv: 2605.14485 · arxiv_version: 2605.14485v1 · doi: 10.48550/arxiv.2605.14485 · pith_short_12: TB53WWDIMHXD · pith_short_16: TB53WWDIMHXDOFWA · pith_short_8: TB53WWDI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TB53WWDIMHXDOFWAA75QP3P2VN \
  | 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: 987bbb586861ee3716c007fb07edfaab5653147975de40c8050fb7b63f0bac07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9454751615741bca1b91bd39c18c85b155e0f145fa3f2c61a7fd160a8a83976c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "econ.TH",
    "submitted_at": "2026-05-14T07:25:52Z",
    "title_canon_sha256": "631ee5f63a49af39655ae58509f3c3e93e1181475ca94e91413b4718f827cc2c"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}