Equilibria in auctions can be very difficult to analyze, beyond the symmetric environments where revenue equivalence renders the analysis straightforward. This paper takes a robust approach to evaluating the equilibria of auctions. Rather than identify the equilibria of an auction under specific environmental conditions, it considers worst-case analysis, where an auction is evaluated according to the worst environment and worst equilibrium in that environment. It identifies a non-equilibrium property of auctions that governs whether or not their worst-case equilibria are good for welfare and revenue. This property is easy to analyze, can be refined from data, and composes across markets where multiple auctions are run simultaneously.

翻译：拍卖中的均衡分析可能非常困难，尤其是在对称环境之外——收入等价定理使对称环境下的分析较为直接。本文采用稳健方法评估拍卖均衡。并非在特定环境条件下识别拍卖的均衡，而是考虑最坏情况分析，即根据最坏环境及该环境下的最坏均衡来评估拍卖。本文识别出拍卖的一个非均衡性质，该性质决定了其最坏情况均衡是否有利于福利和收入。这一性质易于分析，可从数据中提炼，并适用于多个拍卖同时运行的市场组合。