The Shared Discovery Paradox: How a One-Answer Rule Turns Better Information into Worse Search
2026-07-20 • Artificial Intelligence
Artificial IntelligenceComputer Science and Game TheoryMultiagent Systems
AI summaryⓘ
The authors study how groups search for a target by sharing noisy clues. They show that while combining information into one top guess improves accuracy, making everyone follow that single guess lowers the group's overall success. By coordinating diverse search actions or using special rewards, the group can do better. The authors also explore how self-interested behavior and report correlations affect outcomes, providing a detailed model to understand the trade-offs between information sharing, strategies, and incentives.
information poolingsearch problemcoordinationNash equilibriumprice of anarchyprivate signalsincentive designcommon-cue modeldiscovery problem
Authors
Yohei Nakajima
Abstract
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.