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Source note3 min read

The Shared Discovery Paradox: How a One-Answer Rule Turns Better Information into Worse Search

Source

arXiv

arxiv.org/abs/2607.18045v1

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Plain-Language Brief

The study presents a model that examines how organizations pool dispersed information for decision-making in a discovery problem. It finds that while centralized decision-making can improve beliefs, it may also reduce overall coverage due to the one-answer rule. The study also explores other game scenarios and introduces a latent common-cue model.

What the Document Says

  • The text discusses a model where organizations pool dispersed information for decision-making in a discovery problem
  • Centralized decision-making can improve beliefs but reduce overall coverage due to the one-answer rule
  • A coordinated eight-action portfolio using the same pooled reports reaches a higher discovery rate than repeating the top recommendation
  • The study replaces the planner with self-interested searchers who split a prize and introduces an anonymous symmetric equilibrium obeying a water-filling rule
  • The exact mixed price of anarchy is 2 - 1/N in the equal-split game
  • A sole-rescue reward makes every pure Nash equilibrium first-best
  • The study also presents a latent common-cue model that shows how correlated reports collapse effective discovery channels
  • Centralized planner gain rises strictly with copying, and in the canonical environment the symmetric market overtakes decentralized report-following at copying probability c = 0.788462
  • In a proportional large-market limit, the five-protocol ordering survives exactly: consensus discovery vanishes while blind, market, private, and portfolio search converge to specific rates

Key Concepts Mentioned

  • Dispersed information
  • Decentralized clue-following
  • One-answer rule
  • Pooling
  • Coordinated actions
  • Anonymous symmetric equilibrium
  • Water-filling rule
  • Equal-split game
  • Mixed price of anarchy
  • Sole-rescue reward
  • Pure Nash equilibrium
  • Latent common-cue model
  • Centralized planner
  • Copying probability
  • Proportional large-market limit

Claims Made by the Document

  • Centralized decision-making can improve beliefs but reduce overall coverage due to the one-answer rule
  • A coordinated eight-action portfolio using the same pooled reports reaches a higher discovery rate than repeating the top recommendation
  • The exact mixed price of anarchy is 2 - 1/N in the equal-split game
  • A sole-rescue reward makes every pure Nash equilibrium first-best
  • In a proportional large-market limit, the five-protocol ordering survives exactly: consensus discovery vanishes while blind, market, private, and portfolio search converge to specific rates

Evidence Used

  • Data from an exactly solvable benchmark with sixteen boxes, one target, eight searchers, and noisy private clues
  • Simulation results showing the impact of centralized decision-making, coordinated actions, and other game scenarios

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

Organizations often pool dispersed information into one ranking and then allow many agents to act on that shared view. In a discovery problem, this can improve beliefs while reducing coverage. We develop an exactly solvable benchmark with sixteen boxes, one target, eight searchers, and noisy private clues. Pooling raises the accuracy of the best single recommendation from 0.20 to 0.3835, but repeating that recommendation lowers group discovery from 0.8322 under decentralized clue-following to 0.3835. A coordinated eight-action portfolio using the same pooled reports reaches 0.8594, and seven coordinated actions recover the decentralized benchmark. The paradox is a protocol failure, not an information failure: a one-answer rule compresses a portfolio of available actions into one repeated choice. We then replace the planner with self-interested searchers who split a prize. The equal-split game is a potential game. Its anonymous symmetric equilibrium obeys a water-filling rule. In the canonical instance it achieves 0.5991: strictly above consensus, but below both private search and the planner. The exact mixed price of anarchy is 2 - 1/N. A sole-rescue reward, which pays only an agent who covers the target alone, makes every pure Nash equilibrium first-best. Finally, a latent common-cue model shows how correlated reports collapse effective discovery channels. The centralized planner gain rises strictly with copying, and in the canonical environment the symmetric market overtakes decentralized report-following at copying probability c = 0.788462. In a proportional large-market limit the five-protocol ordering survives exactly: consensus discovery vanishes while blind, market, private, and portfolio search converge to 0.500, 0.547, 0.847, and 0.874. The contribution is a compact benchmark that separates information, allocation, incentives, and dependence into exact, reusable quantities.