Pith Number

pith:FMZZ3TOJ

pith:2026:FMZZ3TOJQQLPOKXKSPPJ2Y2JOC

not attested not anchored not stored refs resolved

Watermarking Game-Playing Agents in Perfect-Information Extensive-Form Games

Fei Fang, Juho Kim, Tuomas Sandholm

Game strategies in perfect-information extensive-form games can be watermarked for statistical detection while bounding expected utility loss.

arxiv:2605.14283 v1 · 2026-05-14 · cs.GT · cs.AI · cs.CR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FMZZ3TOJQQLPOKXKSPPJ2Y2JOC}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

We show that the degradation in the quality of the watermarked strategy profile, quantified by the expected utility, can be bounded, but there is a tradeoff between detectability and quality.

C2weakest assumption

The adaptation assumes that the strategy profile in a perfect-information extensive-form game can be modified by embedding a watermark pattern without violating the information structure or equilibrium properties of the original game.

C3one line summary

Adapting the KGW watermark to game strategies in extensive-form games enables statistical detection of watermarked agents with bounded expected-utility degradation.

References

24 extracted · 24 resolved · 0 Pith anchors

[1] N. Brown and T. Sandholm. Superhuman AI for heads-up no-limit poker: Libratus beats top professionals.Science, 359(6374):418–424, 2018 2018

[2] N. Brown and T. Sandholm. Superhuman AI for multiplayer poker.Science, 365(6456):885–890, 2019 2019

[3] M. Campbell, A. J. Hoane, Jr., and F. Hsu. Deep Blue.Artificial Intelligence, 134(1):57–83, 2002 2002

[4] C.-C. Chang and I. Echizen. Steganography in game actions.IEEE Access, 13:21029–21042, 2025 2025

[5] Y . Chang, K. Krishna, A. Houmansadr, J. F. Wieting, and M. Iyyer. PostMark: A robust blackbox watermark for large language models. InProceedings of the Conference on Empirical Methods in Natural Lang 2024

Receipt and verification

First computed	2026-05-17T23:39:10.267072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b339dcdc98416f72aea93de9d634970b0f22ccb306898b552ccc55b8d358861

Aliases

arxiv: 2605.14283 · arxiv_version: 2605.14283v1 · doi: 10.48550/arxiv.2605.14283 · pith_short_12: FMZZ3TOJQQLP · pith_short_16: FMZZ3TOJQQLPOKXK · pith_short_8: FMZZ3TOJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FMZZ3TOJQQLPOKXKSPPJ2Y2JOC \
  | 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: 2b339dcdc98416f72aea93de9d634970b0f22ccb306898b552ccc55b8d358861

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b34ca34670439f523db35b24382462e652c784a2d678a0da8eef893fd4097a1",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-05-14T02:33:30Z",
    "title_canon_sha256": "8ab5b1aa99d77f5ea01f4078356c8762c03b5d1a1f6c70b133482b1a4db04116"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14283",
    "kind": "arxiv",
    "version": 1
  }
}