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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 introduces a benchmark to analyze the Shared Discovery Paradox, a phenomenon where pooling information for one ranking leads to improved beliefs but reduced coverage in a discovery problem. The paradox arises when a one-answer rule compresses multiple available actions into repeated choices, leading to suboptimal results.

What the Document Says

  • The study focuses on the Shared Discovery Paradox, where pooling dispersed information can improve beliefs while reducing coverage in a discovery problem.
  • The benchmark consists of 16 boxes, one target, 8 searchers, and noisy private clues.
  • Pooling information improves the accuracy of the best single recommendation but lowers group discovery.
  • A coordinated eight-action portfolio using the pooled reports can improve group discovery.
  • The paradox is due to a one-answer rule that compresses a portfolio of available actions into one repeated choice.
  • The study also investigates an equal-split game with self-interested searchers, which shows a water-filling rule in the symmetric equilibrium.
  • 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 latent common-cue model shows how correlated reports can collapse effective discovery channels.
  • The study provides a compact benchmark to separate information, allocation, incentives, and dependence into exact, reusable quantities.

Key Concepts Mentioned

  • Shared Discovery Paradox
  • benchmark
  • pooling
  • one-answer rule
  • discovery problem
  • information failure
  • protocol failure

Claims Made by the Document

  • Pooling improves the accuracy of the best single recommendation but lowers group discovery.
  • A coordinated eight-action portfolio can improve group discovery.
  • The equal-split game has a water-filling rule in its symmetric equilibrium.
  • A sole-rescue reward makes every pure Nash equilibrium first-best.
  • Correlated reports can collapse effective discovery channels.

Evidence Used

  • Improvement and reduction of group discovery are demonstrated through numerical examples in the study.
  • The water-filling rule is derived mathematically in the equal-split game.
  • The exact mixed price of anarchy is presented analytically.
  • Simulations and mathematical analyses support the claims about the latent common-cue model.

Methods / Approach

UNKNOWN

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

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Open Questions

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Notes for Future Q&A

May include interpretation. Labeled where it does.

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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.