Pith Number

pith:PJVFO4FH

pith:2026:PJVFO4FHLO7KM5C27DDKY3RXJO

not attested not anchored not stored refs resolved

Meta-Bayesian Nash Equilibrium: Existence via Kakutani's Fixed Point Theorem

Esmaiel Abounoori, Madjid Eshaghi Gordji, Mohamadali Berahman

Meta-Bayesian Nash equilibrium exists when each transformed game has a unique Bayesian Nash equilibrium.

arxiv:2605.16926 v1 · 2026-05-16 · econ.TH · econ.GN · q-fin.EC

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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

Using Kakutani's fixed point theorem, we establish existence under finiteness assumptions on type spaces, meta-actions, and transformations, together with the assumption that each transformed game admits a unique Bayesian Nash equilibrium.

C2weakest assumption

The assumption that each transformed game admits a unique Bayesian Nash equilibrium (stated in the abstract as a prerequisite for applying Kakutani's theorem to the meta-game).

C3one line summary

Defines meta-Bayesian Nash equilibrium for incomplete information and proves existence via Kakutani's fixed point theorem assuming finite type spaces, meta-actions, transformations, and unique Bayesian Nash equilibria in transformed games.

References

10 extracted · 10 resolved · 1 Pith anchors

[1] 2026 , note = 2026

[2] Nash, John F. , title =. Annals of Mathematics , volume =

[3] and Selten, Reinhard , title =

[4] Schelling, Thomas C. , title =

[5] North, Douglass C. , title =

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:03:31.040861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a6a5770a75bbea6745af8c6ac6e374ba3a289801b4bb2c4378a75a385e81c52

Aliases

arxiv: 2605.16926 · arxiv_version: 2605.16926v1 · doi: 10.48550/arxiv.2605.16926 · pith_short_12: PJVFO4FHLO7K · pith_short_16: PJVFO4FHLO7KM5C2 · pith_short_8: PJVFO4FH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PJVFO4FHLO7KM5C27DDKY3RXJO \
  | 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: 7a6a5770a75bbea6745af8c6ac6e374ba3a289801b4bb2c4378a75a385e81c52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86bc4345572d14a9db8f813cb56356ff9b56388548bb9426e10a2c15ad925d28",
    "cross_cats_sorted": [
      "econ.GN",
      "q-fin.EC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "econ.TH",
    "submitted_at": "2026-05-16T10:37:06Z",
    "title_canon_sha256": "94b3f2d0455aca546a3b69d38503df9d2939c324360a8835a201d2b41b355049"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16926",
    "kind": "arxiv",
    "version": 1
  }
}