We consider a multi-agent delegation mechanism without money. In our model, given a set of agents, each agent has a fixed number of solutions which is exogenous to the mechanism, 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. In stark contrast to single-agent setting by Kleinberg and Kleinberg (EC'18) with an approximate Bayesian mechanism, we show that there exists 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 delegation 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：我们考虑一个无货币的多智能体委托机制。在该模型中，给定一组智能体，每个智能体拥有机制外部给定的固定数量解决方案，并私下向委托人发送信号（例如，解决方案的子集）。随后，委托人根据智能体的信号选择最终解决方案。与Kleinberg和Kleinberg（EC'18）在单智能体环境中使用的近似贝叶斯机制形成鲜明对比的是，我们证明了由于智能体之间的竞争张力，存在兼具信息增益和性能增益的高效近似先验无关机制。然而有趣的是，这种竞争性力量的大小显著依赖于智能体可获得的信息量，以及委托人与智能体效用之间的关联程度。在技术层面，我们对多智能体委托问题进行了全面研究，推导出在完全/不完全信息环境下，贝叶斯机制与先验无关机制的近似比相关结果。作为一个具有独立意义的特例，我们获得了关于智能体数量的比较静态分析，结果表明在委托人效用方面，多智能体环境（n≥2）优于单智能体环境（n=1）。我们进一步扩展了问题，考虑机制的审查成本，并在完全信息环境下推导出一些类比结果。