We develop a versatile new methodology for multidimensional mechanism design that incorporates side information about agent types with the bicriteria goal of generating high social welfare and high revenue simultaneously. Side information can come from a variety of sources -- examples include advice from a domain expert, predictions from a machine-learning model trained on historical agent data, or even the mechanism designer's own gut instinct -- and in practice such sources are abundant. In this paper we adopt a prior-free perspective that makes no assumptions on the correctness, accuracy, or source of the side information. First, we design a meta-mechanism that integrates input side information with an improvement of the classical VCG mechanism. The welfare, revenue, and incentive properties of our meta-mechanism are characterized by a number of novel constructions we introduce based on the notion of a weakest competitor, which is an agent that has the smallest impact on welfare. We then show that our meta-mechanism -- when carefully instantiated -- simultaneously achieves strong welfare and revenue guarantees that are parameterized by errors in the side information. When the side information is highly informative and accurate, our mechanism achieves welfare and revenue competitive with the total social surplus, and its performance decays continuously and gradually as the quality of the side information decreases. Finally, we apply our meta-mechanism to a setting where each agent's type is determined by a constant number of parameters. Specifically, agent types lie on constant-dimensional subspaces (of the potentially high-dimensional ambient type space) that are known to the mechanism designer. We use our meta-mechanism to obtain the first known welfare and revenue guarantees in this setting.

翻译：我们提出了一种灵活的新型多维机制设计方法，该方法整合了关于智能体类型的辅助信息，旨在同时实现高社会福利和高收益的双指标目标。辅助信息可源自多种渠道——例如领域专家的建议、基于历史智能体数据训练的机器学习模型的预测，甚至机制设计者自身的直觉判断——而在实际场景中此类信息源非常丰富。本文采用免先验视角，不对辅助信息的正确性、精确性或来源做任何假设。首先，我们设计了一个元机制，将输入的辅助信息与经典VCG机制的改进相结合。该元机制的福利、收益及激励属性通过我们引入的一系列基于“最弱竞争者”（即对福利影响最小的智能体）概念的新颖构造得以刻画。随后证明，当该元机制经过谨慎实例化后，能同时实现由辅助信息误差参数化的强福利与收益保障。当辅助信息高度充分且精确时，该机制的福利与收益可媲美社会总剩余，且其性能随辅助信息质量下降而连续平滑地衰减。最后，我们将元机制应用于每个智能体类型由恒定数量参数决定的场景。具体而言，智能体类型位于（可能高维的）环境类型空间中已知的常维子空间上，我们利用该元机制首次在此场景下获得了福利与收益保障结果。