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REVIEW 3 major objections 1 cited by

The information states and dynamic programming equations derived for delayed-sharing team decisions in the 2023 paper are incorrect.

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2026-06-29 20:51 UTC pith:FO5AD66S

load-bearing objection This correction note flags errors in the 2023 DP recursions for delayed-sharing teams but supplies no proof details or derivation steps, leaving the claims as assertions. the 3 major comments →

arxiv 2605.25700 v1 pith:FO5AD66S submitted 2026-05-25 math.OC

Comments and Corrections on the DP Equations of Paper "On Team Decision Problems With Nonclassical Information Structures"

Charalambos D. Charalambous , Umarbek Guvercin , Seddik Djouadi This is my paper
classification math.OC
keywords team decision problemsnonclassical information structuresdynamic programmingperson-by-person optimalitydelayed sharinginformation statesproof corrections
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This note establishes that the proof of Theorem 5 and the dynamic programming equations (57) and (58) of Theorem 7 in the 2023 paper contain errors. These errors arise from the use of incorrect information states and the assumption that separated strategies are optimal under the delayed-sharing pattern. As a direct result, Lemma 8, Theorem 6, and the complete statement of Theorem 7 become invalid. The note supplies the correct dynamic programming equations based on person-by-person optimality to replace the flawed recursions.

Core claim

The proofs of Theorem 5 and the DP equations (57), (58) of Theorem 7 in the 2023 paper are incorrect. Consequently, Lemma 8, Theorem 6, and the full statement of Theorem 7 are invalid, because their proofs rely on erroneous information states and the optimality of separated strategies. Correct DP equations for PbP optimality are provided.

What carries the argument

Person-by-person optimality from static team theory applied to derive separated dynamic programming recursions for the delayed-sharing information pattern.

Load-bearing premise

Person-by-person optimality from static team theory extends directly to derive separated dynamic programming recursions for delayed-sharing patterns without extra conditions on the filtration or cost structure.

What would settle it

Compute the true conditional expectations for a simple two-player delayed-sharing example and verify whether they satisfy the information-state recursions stated in the 2023 paper.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The proposed information states fail to capture the actual conditional distributions available to each decision maker.
  • Strategies that depend only on the claimed information states are not guaranteed to be optimal.
  • The dynamic programming solution for the team problem under delayed sharing must use different recursions than those originally presented.
  • Nonclassical information structures require explicit derivation of information states rather than direct transfer from static team results.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The identified gap suggests that separation in dynamic team problems with delays may need extra measurability or integrability conditions.
  • Similar proof issues could appear in other delayed or partial-sharing patterns not covered by the original work.
  • Verification of DP recursions through low-dimensional examples would be a practical next step for any extension of this analysis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 0 minor

Summary. This note asserts that the proof of Theorem 5 (information-state recursions) and the dynamic programming equations (57) and (58) of Theorem 7 in the 2023 paper [1] are incorrect. It concludes that Lemma 8, Theorem 6, and the full statement of Theorem 7 in [1] are therefore invalid because their proofs rely on the erroneous information states and on the optimality of separated strategies. The note states that it supplies corrected DP equations for person-by-person optimality under delayed-sharing patterns.

Significance. If the claimed errors were demonstrated and the corrected recursions derived in detail, the note would clarify technical subtleties in the analysis of nonclassical information structures for dynamic team problems. At present the manuscript supplies neither the location of the error inside the proofs of [1] nor the derivation steps leading to the asserted corrections, so the significance of the contribution cannot be assessed from the given text.

major comments (3)
  1. [Abstract / Introduction] The central claim—that the proof of Theorem 5 and eqns (57)–(58) of Theorem 7 in [1] are incorrect—rests on an assertion without any quoted passage, step-by-step identification of the flaw, or counter-example showing where the information-state recursion or separated-strategy optimality fails. No section of the note supplies this evidence.
  2. [Abstract] The further claim that Lemma 8, Theorem 6 and the full Theorem 7 of [1] are invalidated is not supported by any explicit tracing of dependence: the note does not exhibit the first invocation of the asserted erroneous recursion inside those later proofs.
  3. [Abstract] The manuscript states that it provides 'the correct DP equations' but does not display the derivation of those equations or the technical conditions under which they hold, leaving the corrected statements unverified.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We will revise the manuscript to supply the requested details on the location of the errors, explicit dependence tracing, and derivations of the corrected equations.

read point-by-point responses

  1. Referee: [Abstract / Introduction] The central claim—that the proof of Theorem 5 and eqns (57)–(58) of Theorem 7 in [1] are incorrect—rests on an assertion without any quoted passage, step-by-step identification of the flaw, or counter-example showing where the information-state recursion or separated-strategy optimality fails. No section of the note supplies this evidence.

    Authors: We agree that the current concise note does not quote specific passages or provide a counter-example. The revised version will add a dedicated section that quotes the relevant steps from the proof of Theorem 5 in [1], identifies the precise flaw in the information-state recursion, and supplies a counter-example demonstrating the failure of separated-strategy optimality. revision: yes

  2. Referee: [Abstract] The further claim that Lemma 8, Theorem 6 and the full Theorem 7 of [1] are invalidated is not supported by any explicit tracing of dependence: the note does not exhibit the first invocation of the asserted erroneous recursion inside those later proofs.

    Authors: We acknowledge the need for explicit dependence tracing. In the revision we will map the first use of the erroneous information states and separated strategies within the proofs of Lemma 8, Theorem 6, and Theorem 7 of [1], thereby rigorously establishing the scope of invalidation. revision: yes

  3. Referee: [Abstract] The manuscript states that it provides 'the correct DP equations' but does not display the derivation of those equations or the technical conditions under which they hold, leaving the corrected statements unverified.

    Authors: The note is intended as a brief comment, yet we recognize that verification requires the derivation. The revised manuscript will include the full step-by-step derivation of the corrected person-by-person optimality equations for delayed-sharing patterns together with the precise technical conditions under which they hold. revision: yes

Circularity Check

0 steps flagged

External critique of [1] with independent claims; no self-referential reduction

full rationale

The paper identifies errors in the proof of Theorem 5 and DP equations (57)-(58) of Theorem 7 in external reference [1], then asserts consequent invalidity of Lemma 8, Theorem 6 and full Theorem 7 because those proofs rely on the claimed erroneous information states and separated strategies. It further states it provides correct DP equations for PbP optimality. None of these steps reduce by construction to quantities defined inside this paper (no fitted parameters, no self-citation load-bearing uniqueness theorems, no ansatz smuggled via own prior work). The derivation chain targets [1]'s content and is self-contained against external benchmarks; the note does not rename its own inputs as predictions or invoke its own prior results to force its conclusions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The note relies on standard assumptions of stochastic team theory (existence of conditional expectations, measurability of strategies, and the definition of person-by-person optimality) that are inherited from the prior literature rather than newly postulated.

axioms (2)
  • standard math Conditional expectations and filtrations are well-defined for the delayed-sharing information pattern
    Invoked when discussing information states and separation of strategies
  • domain assumption Person-by-person optimality is the appropriate solution concept for the dynamic team problem
    Used to justify the form of the target DP equations

pith-pipeline@v0.9.1-grok · 5731 in / 1318 out tokens · 23522 ms · 2026-06-29T20:51:53.759426+00:00 · methodology

0 comments
read the original abstract

The 2023 paper ``On Team Decision Problems With Nonclassical Information Structures'' [1] presented information states and dynamic programming (DP) equations for delayed sharing information patterns, based on the concept of person-by-person (PbP) optimality of static team theory. In particular, [Section IV, 1], Theorem 5 presents recursions of the information states and Theorem 7, eqn(57), eqn(58), presents DP equations, of each team member. In this note we show that the proof of Theorem 5 and the DP eqn(57), eqn(58) of Theorem 7 of [1] are incorrect. Consequently, Lemma 8, Theorem 6, and the full statement of Theorem 7 in [1] are invalid, because their proofs rely on erroneous information states and the optimality of separated strategies (i.e., functions of the information states). We further provide the correct DP equations for PbP optimality, thereby highlighting the subtleties and challenges inherent in the analysis of delayed sharing information patterns.

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Private & Common Information States in Decentralized Team Equilibrium via Dynamic Programming for POMDPs with Delayed Sharing

    eess.SY 2026-05 unverdicted novelty 7.0

    Derives DP equations and structural compression for decentralized team equilibria in delayed-sharing POMDPs, extending Witsenhausen's 1971 assertions with private and common information states.

Reference graph

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14 extracted references · 1 canonical work pages · cited by 1 Pith paper · 1 internal anchor

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    work page internal anchor Pith review Pith/arXiv arXiv 2026