Pith Number

pith:RBLHGNEW

pith:2026:RBLHGNEWKKA7XNINHQTDPJYAPL

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Convergence of Stochastic First-Order Algorithms in Bertrand Competition Under Incomplete Information

Jan-Sebastian Hoehener, Martin Bichler

Euclidean RRM algorithms converge almost surely to the unique efficient Bayes-Nash equilibrium in finite-dimensional approximations of Bayesian Bertrand competition.

arxiv:2605.17607 v1 · 2026-05-17 · cs.GT

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Claims

C1strongest claim

we prove that Euclidean RRM algorithms converge almost surely to the unique, efficient Bayes-Nash equilibrium within a finite-dimensional approximation of the strategy space.

C2weakest assumption

The strategy space admits a finite-dimensional approximation by symmetric piecewise-linear pricing functions for which a global Lyapunov function can be explicitly constructed (abstract, paragraph on duopoly analysis).

C3one line summary

Euclidean RRM algorithms converge almost surely to the unique efficient Bayes-Nash equilibrium in a finite-dimensional approximation of Bayesian Bertrand competition with private costs.

References

21 extracted · 21 resolved · 0 Pith anchors

[1] The art of retail pricing: Developing a taxonomy for describing pricing algorithms.European Conference on Information Systems, 2024 2024

[2] Online Learning and Online Convex Optimization.Foundations and Trends® in Machine Learning, 4(2):107–194, 2011 2011

[3] Book review of theorie mathematique de la richesse social and of recherches sur les principes mathematiques de la theorie des richesses.Journal des Savants, 1883

[4] Algorithmic Pricing What Implications for Competition Policy?Review of Industrial Organization, 55(1):155–171, aug 2019 2019

[5] Autonomous algorithmic collusion: Q-learning under sequential pricing.The RAND Journal of Economics, 52(3):538–558, 2021 2021

Formal links

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Receipt and verification

First computed	2026-05-20T00:04:48.221385Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

88567334965281fbb50d3c2637a7007ad8efc3327185d9e53783c9233ccf87cd

Aliases

arxiv: 2605.17607 · arxiv_version: 2605.17607v1 · doi: 10.48550/arxiv.2605.17607 · pith_short_12: RBLHGNEWKKA7 · pith_short_16: RBLHGNEWKKA7XNIN · pith_short_8: RBLHGNEW

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RBLHGNEWKKA7XNINHQTDPJYAPL \
  | 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: 88567334965281fbb50d3c2637a7007ad8efc3327185d9e53783c9233ccf87cd

Canonical record JSON

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    "abstract_canon_sha256": "b3f85edc29037bc1a4e1753a4c059cbb3a682cdef3f552d08342f57d3695f230",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2026-05-17T19:08:32Z",
    "title_canon_sha256": "be04aacfdbe4a056e4944e4baf1af01341c7a01bffcd0204ed9f9c676731a081"
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    "kind": "arxiv",
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