Pith Number

pith:PWN2JTKC

pith:2026:PWN2JTKCDOADJX4N7MQD5I4TYL

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On the Complexity of Correlated Equilibria Beyond Normal-Form Games

Brian Hu Zhang, Constantinos Daskalakis, Gabriele Farina, Ioannis Anagnostides, Noah Golowich, Tuomas Sandholm

Computing a correlated equilibrium in concave quadratic games is as hard as computing the fixed point of a contraction mapping.

arxiv:2605.17665 v1 · 2026-05-17 · cs.GT

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4 Citations open

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Claims

C1strongest claim

computing a correlated equilibrium in concave quadratic games is as hard as computing the fixed point of a contraction mapping (Contr), providing the first strong evidence of intractability.

C2weakest assumption

The reduction establishing Contr-hardness for correlated equilibria holds specifically for the class of concave quadratic games and for the standard definition of correlated equilibrium; if the game class or equilibrium notion is altered, the hardness may not transfer (abstract statement on hardness for concave quadratic games).

C3one line summary

The paper establishes Contr-hardness for correlated equilibria in concave quadratic games, an exponential lower bound on swap regret minimization, and FPTAS algorithms for poly-dimensional Φ-equilibria in concave games.

References

81 extracted · 81 resolved · 0 Pith anchors

[1] First-order (coarse) correlated equilibria in non-concave games 2026

[2] On the complexity of computing sparse equilibria and lower bounds for no-regret learning in games 2024

[3] Pareto-optimal algorithms for learning in games 2024

[4] Swap regret and correlated equilibria beyond normal-form games 2025

[5] On the value of correlation 2008

Receipt and verification

First computed	2026-05-20T00:04:51.662523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d9ba4cd421b8034df8dfb203ea393c2d4d10aa96e8f79814d432f5706e4b0d7

Aliases

arxiv: 2605.17665 · arxiv_version: 2605.17665v1 · doi: 10.48550/arxiv.2605.17665 · pith_short_12: PWN2JTKCDOAD · pith_short_16: PWN2JTKCDOADJX4N · pith_short_8: PWN2JTKC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PWN2JTKCDOADJX4N7MQD5I4TYL \
  | 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: 7d9ba4cd421b8034df8dfb203ea393c2d4d10aa96e8f79814d432f5706e4b0d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d64e8e8f5ea4c09749a13f769fb9da4da2d715d9a304e8ae946ea0553f91ba6b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-05-17T21:50:52Z",
    "title_canon_sha256": "60e8076d832e0d5fd5a5f0ebeaf8b760a22cc1c381d263d60ed6ef4c55d1f39c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17665",
    "kind": "arxiv",
    "version": 1
  }
}