Yohei Nakajima's Shared Discovery Paradox: Better info can hurt group search
Pooling data boosts single accuracy by 92% but slashes group discovery by 54%
Yohei Nakajima's latest paper, "The Shared Discovery Paradox," exposes a counterintuitive failure mode in how organizations use pooled information. In a toy benchmark of 16 boxes, one target, eight searchers, and noisy private clues, consolidating all data into a single ranked recommendation raises the accuracy of the best single guess from 0.20 to 0.3835—a 92% improvement. However, when all agents act on that same top recommendation, group discovery (the probability someone finds the target) plummets from 0.8322 under decentralized clue-following to just 0.3835. The system knows more, but searches less effectively because diversity of action is lost. Nakajima shows this is a protocol failure, not an information failure: a one-answer rule compresses a rich portfolio of possible actions into a single repeated choice. A coordinated eight-action portfolio that uses the same pooled reports achieves 0.8594, and even seven coordinated actions recover the decentralized benchmark of 0.8322.
The paper then extends the analysis to incentive structures. Replacing a central planner with self-interested searchers who split a prize equally leads to an anonymous symmetric equilibrium with a water-filling rule, reaching 0.5991—strictly above consensus (0.3835) but below both private search (0.8322) and the planner's optimum. The exact mixed price of anarchy is 2 - 1/N. Introducing a "sole-rescue" reward that pays only an agent who finds the target alone makes every pure Nash equilibrium first-best. Nakajima also models correlated reports via a latent common-cue factor, showing that as copying probability c increases, centralized planner gain rises strictly. At c = 0.788462 the symmetric market overtakes decentralized report-following. In a proportional large-market limit, five protocols collapse to exact values: consensus (0), blind (0.500), market (0.547), private (0.847), and portfolio (0.874). The contribution is a compact benchmark separating information, allocation, incentives, and dependence into reusable quantities.
- Consolidating all data into one top recommendation boosts single accuracy from 0.20 to 0.3835 but cuts group discovery from 0.8322 to 0.3835
- A coordinated eight-action portfolio using the same pooled data achieves 0.8594, proving the loss is due to protocol, not information
- With self-interested searchers splitting a prize equally, discovery reaches 0.5991; a sole-rescue reward restores first-best outcomes
Why It Matters
Organizations relying on top-K recommendations risk halving discovery—diversity of action is as critical as data quality.