We consider a multi-agent delegated search without money, which is the first to study the multi-agent extension of Kleinberg and Kleinberg (EC'18). In our model, given a set of agents, each agent samples a fixed number of solutions, and privately sends a signal, e.g., a subset of solutions, to the principal. Then, the principal selects a final solution based on the agents' signals. Our model captures a variety of real-world scenarios, spanning classical economical applications to modern intelligent system. In stark contrast to single-agent setting by Kleinberg and Kleinberg (EC'18) with an approximate Bayesian mechanism, we show that there exist efficient approximate prior-independent mechanisms with both information and performance gain, thanks to the competitive tension between the agents. Interestingly, however, the amount of such a compelling power significantly varies with respect to the information available to the agents, and the degree of correlation between the principal's and the agent's utility. Technically, we conduct a comprehensive study on the multi-agent delegated search problem and derive several results on the approximation factors of Bayesian/prior-independent mechanisms in complete/incomplete information settings. As a special case of independent interest, we obtain comparative statics regarding the number of agents which implies the dominance of the multi-agent setting ($n \ge 2$) over the single-agent setting ($n=1$) in terms of the principal's utility. We further extend our problem by considering an examination cost of the mechanism and derive some analogous results in the complete information setting.

翻译：我们研究无货币的多智能体委托搜索问题，这是首次对Kleinberg和Kleinberg (EC'18) 的多智能体扩展进行探索。在我们的模型中，给定一组智能体，每个智能体采样固定数量的解，并私下向委托方发送信号（例如，解的某个子集）。随后，委托方根据智能体的信号选择最终解。该模型涵盖了从经典经济学应用到现代智能系统的多种现实场景。与Kleinberg和Kleinberg (EC'18) 在单智能体设置中采用近似贝叶斯机制形成鲜明对比，我们证明，由于智能体间的竞争张力，存在高效的近似先验无关机制，能够同时带来信息增益和性能提升。然而有趣的是，这种竞争力量的大小显著依赖于智能体可获得的信息量，以及委托方与智能体效用之间的相关程度。在技术层面，我们对多智能体委托搜索问题进行了全面研究，推导出关于完全信息/不完全信息环境下贝叶斯/先验无关机制近似比的若干结果。作为独立感兴趣的特例，我们获得了关于智能体数量的比较静态分析，结果表明多智能体设置（n≥2）在委托方效用方面优于单智能体设置（n=1）。我们还进一步考虑了机制的检验成本，在完全信息设定下得到了类似的结果。