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When Does Information Sharing Improve Decentralized Discovery? Aggregation, Independent Rescue, and Equilibrium Selection

Yohei Nakajima

arXiv:2609.01814v1cs.AIcs.GT

TL;DR

The paper asks when information sharing improves discovery despite removing independent rescue actions. It uses exact finite discovery models, action-budget comparisons, a residual-error frontier, and a binary Bayesian game to separate aggregation from capacity loss and implementation. Sharing improves discovery under the registered protocol when residual error contracts beyond the rescue threshold, while the strategic positive interval remains dependent on selected equilibria.

  • Problem

    Information sharing can improve a pooled estimate while eliminating independent rescue actions, so posterior accuracy alone does not determine portfolio discovery.

  • Method

    The paper combines centralized action-budget profiles, a registered incremental-sharing identity, finite channel registries, and a binary Bayesian game.

  • Results

    Sharing helps exactly when pooled residual error contracts faster than rescue capacity, while the selected strategic result is positive only for named equilibrium selections.

  • Takeaways & Limitations

    Evaluate sharing using residual error, surviving independent actions, action authority, and the equilibrium or behavioral rule being compared.

  • Takeaways & Limitations

    The models are finite and synthetic, with a binary two-agent strategic setting, fixed p = 3/5, independent rescue assumptions, truthful costless sharing, and no welfare claim beyond registered discovery and payoff objects.

Abstract

from arXiv · show

Information sharing can improve a pooled estimate while eliminating independent rescue actions. This paper separates those effects in exact finite discovery models. A centralized action-budget profile shows that equal one-person accuracy can coexist with different portfolio values. Under a registered incremental-sharing protocol, a sharing step improves discovery exactly when pooled residual error contracts faster than an independent rescue attempt. Exact bounded registries exhibit compression, aggregation, neutral curves, and a bounded zero mixed class. In a two-agent Bayesian game with a hidden mixture of common and independent signal sources, the registered selected equilibrium yields a strict positive sharing interval at signal accuracy 3/5, while alternative equilibria show that the result is selection-dependent rather than universal. The models are synthetic and finite; no human or organizational data are used.

1 Introduction

The paper separates the aggregation benefit of information sharing from the independent rescue capacity pooling removes. It develops exact finite models and shows that decentralized gains depend on residual-error contraction and equilibrium selection.

  • Motivation: The paper compares pooled accuracy with portfolio discovery, because sharing can improve one common action while eliminating independent rescue attempts.The relevant question is whether aggregation gains compensate for the search capacity absorbed by pooling.
  • Framework: The analysis combines action-budget profiles, an incremental-sharing identity, a residual-error frontier, and a binary Bayesian game.These layers compare centralized recovery, registered rescue protocols, and decentralized implementation.
  • Sharing frontier: Sharing helps exactly when pooled residual error contracts faster than an independent rescue attempt, is neutral at equality, and hurts above the threshold.Under the registered protocol, the condition is es+1/es < 1 −q.
  • Strategic implementation: At signal accuracy 3/5, a registered selected equilibrium yields a strict positive sharing interval, but the result is not universal across equilibria.Alternative private and ownership-aware strategies, plus a centralized top-two benchmark, qualify the interpretation.
  • Finite findings: Equal one-person accuracy can coexist with different portfolio values, recovery budgets, and sharing directions.The bounded registry also contains compression, aggregation, and all-neutral curves, while preserving a bounded zero mixed class.
  • Contribution: The paper presents a theorem-family synthesis with self-contained identities and verified bounded computations rather than a new foundational novelty claim.Its comparisons distinguish centralized benchmarks, decentralized protocols, selected equilibria, and alternative equilibria.

2 Discovery architectures and comparison baselines

The paper distinguishes private, pooled-centralized, incremental-sharing, and strategic architectures because information and action authority jointly determine discovery. Equal one-person accuracy and private discovery can still produce different pooled portfolio values and recovery budgets.

  • Architectures: Discovery is the probability that at least one realized action matches the single correct candidate.Agents may act privately, pool signals, or submit them to a planner.
  • Architectures: A direct private baseline maps each agent’s signal to one registered action, with independent randomization for set-valued signals.For shortlists and exclusions, the registered rule randomizes uniformly over the relevant set.
  • Architectures: A centralized action-budget profile measures the best discovery probability obtainable from pooled signals when a planner may take L posterior-ranked actions.V1 captures one common action, whereas higher budgets capture multi-action coverage; these are not decentralized equilibria unless implemented institutionally.
  • Comparisons: Pooled centralized profiles, incremental sharing, and strategic equilibria are different counterfactuals because they assign information and action authority differently.A planner can enforce posterior top-two diversification, while autonomous symmetric agents may duplicate actions or coordinate on constant targets.
  • Comparisons: The noisy point and guaranteed shortlist both have q = 1/2 and P3 = 7/8, yet their pooled profiles differ, so (q, P3) does not determine portfolio value.The computations are finite exact enumerations from the registered model and fixtures.
  • Comparisons: The five registered channel families have exact centralized profiles, and recovery budgets are 3, 2, 1, 2, and 3 for noisy point, noisy shortlist, guaranteed shortlist, exclusion, and confidence point.The guaranteed shortlist recovers its direct baseline with one pooled action, while the noisy point requires three.

4 Aggregation gain and independent rescue

Incremental sharing trades pooled coverage against the independent rescue action it removes. Under the registered protocol, the exact sign is determined by whether pooled residual error contracts faster than private rescue deteriorates, producing channel-specific increasing, decreasing, or neutral paths.

  • Aggregation gain: A pooled block of size s leaves N − s private searchers, whose independent rescue failures occur jointly with probability (1 − q)^(N−s) after a pooled miss.This yields the registered discovery expression for incremental sharing.
  • Aggregation gain: The incremental-sharing identity says the sign of an additional sharing step equals pooled coverage gain net of the private rescue action it replaces.The proof is exact and uses no distributional approximation.
  • Channel paths: The registered noisy-point curve is weakly decreasing, whereas the equally accurate guaranteed-shortlist channel moves in the opposite direction.Thus the sign is channel-specific rather than determined by q = 1/2 alone.
  • Channel paths: At M = 4, N = 3, q = 1/2, the noisy-point path falls from 7/8 to 3/4 to 7/12, while the guaranteed-shortlist path rises from 7/8 to 11/12 to 17/18.Their changes are −1/8, −1/6 versus 1/24, 1/36.
  • Registry: Across 2,044 adjacent transitions in the registered DD-020 grid, 1,848 are negative, 196 neutral, and zero positive; the guaranteed-shortlist row is a counterchannel.The census contains 2,555 protocol rows arranged into 511 parameter chains.

5 The General Sharing Frontier

The exact sharing frontier compares pooled residual-error contraction with the rescue value of an independent action. In the frozen registry, curves are compression-dominated, aggregation-dominated, or all-neutral, with no mixed curve observed within that bounded scope.

  • Exact frontier: ρs < 1 −q makes a sharing step strictly improve discovery, equality is neutral, and ρs > 1 −q makes it reduce discovery.Here ρs is the pooled residual-error contraction ratio and 1 −q is the private rescue threshold.
  • Exact frontier: The frontier explains why noisy-point and guaranteed-shortlist channels with equal q can have opposite sharing directions.Their error-contraction curves fall on opposite sides of the same rescue threshold.
  • Bounded classification: 177 registered scenarios contain 126 strict-compression, 16 strict-aggregation, and 35 all-neutral curves, with stored ratios matching the theorem’s sign in every row.The registry also contains no mixed curve.
  • Scope: The registry is a systematic stress test across finite channel families and parameter values, not a probability sample of real organizations.Its compression, aggregation, and neutral labels describe frozen curves under the registered scope.
  • Bounded classification: The zero mixed count is a bounded negative result, not evidence that arbitrary channels have monotone sharing curves.A mixed curve outside the registry would not contradict the theorem, and unrestricted parameterizations within registered families were not tested.

6 Centralized action-budget recovery

Centralized action budgets separate pooled information from the number of actions available after pooling. Full candidate capacity recovers the direct private baseline, but the minimum required budget varies across registered scenarios.

  • Recovery theorem: A centralized planner can assign several posterior-ranked actions, with top-L coverage VL nondecreasing in L and reaching one at full candidate capacity.This establishes finite recovery under centralized authority.
  • Recovery theorem: L∗≤M always, and L∗=1 exactly when CN = V1 ≥PN.L∗ is the minimum centralized recovery budget needed to match the direct private baseline PN.
  • Scope: The recovery theorem concerns centralized authority and does not imply that decentralized agents will choose distinct actions.Pooling may also be costly or constrained by limited action capacity or competing tasks.
  • Bounded census: The 177-scenario registry has recovery budgets L∗=1, 2, 3, 4 in 51, 55, 64, and 7 scenarios, respectively.Every registered scenario satisfies the full-capacity theorem and stored recovery characterization.
  • Design implication: For 126 scenarios, at least two centralized actions are required, while seven require all four, making information architecture and post-sharing action budget jointly relevant.A binary share-or-not recommendation omits this action-capacity dimension.

7 Coordination-free positive sharing

In the registered two-agent Bayesian game, sharing can strictly improve discovery over selected private play at p = 3/5. The gain is tied to equilibrium selection and does not extend to every equilibrium or strategy in the game.

  • Equilibrium selection: The comparison uses a private anonymous label-equivariant equilibrium and a shared identical-mixing rule based only on the common posterior.These restrictions define exact, reproducible selected objects but are selection assumptions.
  • Positive sharing interval: The same open interval strictly improves expected payoff per agent under the registered selections.This is the payoff counterpart of the selected-discovery comparison.
  • Mechanism: At low dependence, private clues supply diversity while sharing can induce crowding; at higher dependence, selected anti-crowding responses reinforce the sharing gain.At perfect dependence, sharing adds no information relative to identical private clues.
  • Bounded evidence: The registered 7 × 6 grid contains 6 positive, 18 negative, and 18 neutral comparisons, while higher listed accuracies have zero positive cells.These are bounded registered-cell counts, not empirical frequencies or a monotone accuracy law.
  • Equilibrium selection: Alternative equilibria include constant-target private play attaining discovery one and ownership-aware disagreement strategies, so the positive interval is not universal.A centralized top-two planner also strictly dominates the selected shared outcome.

8 Equilibrium selection and implementation failure

The positive sharing result compares named equilibria rather than all equilibria. Alternative strategies and centralized authority can attain discovery one, while truthful sharing does not itself solve strategic disclosure.

  • The positive theorem compares two named equilibria and does not establish improvement for every, best, or worst equilibrium.The qualification is mathematical, not rhetorical.
  • Private play admits opposite constant-target equilibria attaining discovery one for every dependence level.After sharing, ownership-aware disagreement strategies can also assign different targets when clues disagree.
  • Equilibrium selection depends on institutional restrictions such as anonymity, label equivariance, posterior-only strategies, and identical mixing.These restrictions exclude fixed roles, clue ownership, or asymmetric role assignment, but they do not follow merely from sharing information.
  • At p = 3/5, a centralized top-two planner attains V2 = 1 and strictly exceeds the selected shared equilibrium.The planner binds distinct target assignments, unlike decentralized coordination.
  • The current model fixes truthful clue sharing and studies the following action game, leaving strategic disclosure unresolved.Communication may depend on preferences and incentives in other models.

9 Design implications and limitations

The paper recommends diagnosing discovery objectives, residual error, surviving action capacity, and selection authority before evaluating information sharing. Its design implications remain bounded by synthetic finite models and structural assumptions.

  • The diagnostic sequence distinguishes discovery objectives, signal geometry, surviving independent actions, action authority, and the compared equilibrium or behavioral rule.The paper presents this as a diagnostic sequence rather than a universal prescription.
  • If V1 < PN but V2 ≥PN, sharing may be informationally sound while a one-action implementation fails.Possible responses include reserving a second action, maintaining a private red team, or producing a shortlist.
  • Role design can matter as much as disclosure because identifiers, clue ownership, conventions, and assignment authority change the implementable strategy space.Deployment claims should name their selection mechanism rather than report “the equilibrium.”
  • The models do not estimate dynamic learning processes or optimize over all feasible experiments.They take registered channels as given and do not model communication networks or broader information-design optimization.
  • The strategic model is binary, two-agent, uses a specific split-prize payoff, and fixes p = 3/5 with two named equilibrium selections.Other structural limits include independent rescue, truthful costless sharing, no additional information acquisition, and binding centralized actions.
  • No participants, human data, organizational data, or experiment were used; displayed counts are exact enumerations of synthetic model inputs.The authors state that these results should motivate experimental contrasts rather than be described as observations.

10 Conclusion

The paper’s conclusion is conditional: sharing helps when pooled residual error contracts enough to replace lost independent rescue capacity and when the selected decentralized behavior implements that gain. Portfolio values, action capacity, and equilibrium selection therefore remain central to interpretation.

  • Information sharing improves discovery when pooled residual error contracts faster than the independent rescue technology can repair it.The exact frontier is es+1/es < 1 −q.
  • Equal one-person accuracy can coexist with different pooled profiles, recovery budgets, and sharing directions.Full centralized action capacity can recover the private baseline, but the required budget is a design choice.
  • The strategic positive interval belongs to named equilibrium selections rather than constituting a universal information effect.Alternative private and ownership-aware strategies, plus the centralized benchmark, define the boundary of the claim.
  • The residual-error identity follows from a pooled failure event and independent private rescue failures under the registered protocol.Adding one pooled agent removes one remaining rescue action, producing the incremental comparison.
  • The frontier has explicit boundary cases: es = 0 makes the ratio undefined, while q = 1 makes absorbing the last perfect rescuer non-improving.The undivided identity remains valid when es = 0.

B Canonical exact records

The paper’s exact records compare pooled action coverage with lost independent rescue capacity, then extend the comparison to bounded registries and selected equilibria. They distinguish centralized benchmarks and selected outcomes from alternative strategies that can achieve discovery one.

  • Selected equilibria: At ρ ∈ {0, 1/6, 1/4, 1/2, 7/12, 3/4, 1} and p = 3/5, the selected private and shared sequences differ, while the centralized value is one.The selected shared result is therefore a registered equilibrium comparison rather than a universal equilibrium claim.
  • Action-budget profiles: The centralized profile computes VL by summing posterior probabilities over the L highest-ranked candidates, not just the top candidate.The complete posterior vector captures the marginal value of additional actions.
  • Action-budget profiles: Equal top-label accuracy can yield different portfolio values because posterior error may be concentrated on one runner-up or dispersed across candidates.Coverage depends directly on the ordering of remaining posterior masses.
  • Incremental sharing: A sharing step changes both pooled coverage and the number of independent rescue attempts, so holding either component fixed answers a different question.The registered protocol compares block sizes s and s+1 while accounting for the capacity cost of pooling.
  • Incremental sharing: Sharing improves discovery when the pooled block removes a larger share of residual error than one private rescue attempt would remove.The sign is determined by a strict break-even inequality without requiring the absolute level of Gs.
  • Scope of the frontier: The ratio criterion requires independent rescue assumptions, history-invariant rescue quality, and a one-for-one capacity transition; correlated or history-dependent rescue changes require modified failure probabilities.These extensions are not silently covered by DD-C-0097.
  • Bounded registries: Bounded registry labels summarize exact step signs: aggregation dominated, compression dominated, all-neutral, or mixed.The census over 177 rows cannot prove the formula for unenumerated parameters, while the algebraic proof cannot establish that the registry contains a mixed witness.
  • Bounded registries: Minimal witnesses are minimal only under the frozen lexicographic ordering of registered parameters, not among every mathematically possible channel.The qualifier applies to the registry’s tables and generated asset note.

D Evidence, provenance, and reproducibility

The paper documents a reproducibility pipeline that freezes claims, source outputs, hashes, and generated artifacts. Its verification is independent in implementation but not external replication, and the synthesis adds no new study or claim record.

  • Verification pipeline: The generator resolves 22 claim IDs, verifies ten source-output hashes, writes exact figure CSVs and TeX artifacts, and requires byte-identical PDF hashes across two fixed-epoch builds.Artifacts include run IDs, claim IDs, generator information, and input checksum prefixes.
  • Verification scope: Independent verification means a separately implemented repository check that does not import or call the primary generator path.It is explicitly not replication by an unaffiliated external team.
  • Verification scope: The immutable records, verifier outputs, corruption checks, and generator are public at repository commit 66ba4449572b20c519a4629ef20cfc030fae1762.The repository also preserves complete manifest SHA-256 digests for the four run directories.
  • Review artifacts: Review-facing outputs include DD-020 channel profiles, DD-021 registry data, and DD-022 registry data, with verification and corruption-test records in their run directories.The listed artifacts preserve the exact source outputs used for review.
  • Ownership: The manuscript adds no new claim record, study, or run; DD-019 through DD-022 retain ownership of the results they document.Editorial synthesis leaves those ownership lines unchanged.

E Literature boundary

The paper situates its contribution at the intersection of informativeness, decentralized information allocation, social learning, and strategic communication. It presents a specific finite portfolio-and-equilibrium composition without claiming a universal new frontier.

  • Adjacent literatures: Related work covers Blackwell informativeness, team decision theory, herding and social learning, and strategic communication.These literatures motivate narrow contribution language for the present synthesis.
  • Contribution boundary: The paper’s contribution is a particular composition of portfolio objective, rescue technology, coverage profile, and selected action game.That composition does not support a claim that related frontiers, anti-crowding mechanisms, or selection caveats are absent elsewhere.
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