AI 中文总结
研究共享信息时单答案规则导致的发现悖论，通过可精确求解的十六盒模型对比不同情况，指出这是协议失败。还探讨了自利搜索者博弈及共同线索模型，贡献是分离信息等因素为精确可复用量的紧凑基准。
AI 中文摘要
组织通常将分散的信息汇总成一个排名，然后让许多主体据此行动。在发现问题中，这会改善信念但降低覆盖范围。我们开发了一个可精确求解的基准模型，有十六个盒子、一个目标、八个搜索者和有噪声的私人线索。汇总提高了最佳单一推荐的准确性，但重复该推荐会降低群体发现率。协调的八行动组合能达到更高发现率，悖论是协议失败而非信息失败。用自利搜索者取代规划者后，平等分割博弈是潜在博弈，其匿名对称均衡遵循注水规则。单一救援奖励使每个纯纳什均衡达到最优。潜在共同线索模型展示了相关报告如何使有效发现渠道崩溃。贡献是一个紧凑基准，将信息、分配、激励和依赖分离为精确、可重复使用的量。
英文摘要
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.
Comments29 pages, 4 figures. Code, data, and an interactive guide: https://github.com/yoheinakajima/shared-discovery-paradox
