Consider a principal who wants to search through a space of stochastic solutions for one maximizing their utility. If the principal cannot conduct this search on their own, they may instead delegate this problem to an agent with distinct and potentially misaligned utilities. This is called delegated search, and the principal in such problems faces a mechanism design problem in which they must incentivize the agent to find and propose a solution maximizing the principal's expected utility. Following prior work in this area, we consider mechanisms without payments and aim to achieve a multiplicative approximation of the principal's utility when they solve the problem without delegation. In this work, we investigate a natural and recently studied generalization of this model to multiple agents and find nearly tight bounds on the principal's approximation as the number of agents increases. As one might expect, this approximation approaches 1 with increasing numbers of agents, but, somewhat surprisingly, we show that this is largely not due to direct competition among agents.

翻译：考虑一个委托方希望在一个随机解空间中搜索能够最大化其效用的解。若委托方无法独立完成搜索，则可将此问题委托给一个具有不同且可能不一致效用函数的代理方。这被称为委托搜索，委托方在此类问题中面临一个机制设计问题：必须激励代理方找到并提出能够最大化委托方期望效用的解。遵循该领域的先前研究，我们考虑无支付机制，并致力于在委托方不通过委托独立解决问题时，获得其效用的乘性近似。在本研究中，我们探讨了该模型向多智能体场景的自然且近期被研究的扩展，并随着智能体数量的增加，得到了委托方近似比的近乎紧确界。正如预期，该近似比随着智能体数量的增加趋近于1，但令人惊讶的是，我们发现这主要并非源于智能体之间的直接竞争。