This survey outlines a general and modular theory for proving approximation
guarantees for equilibria of auctions in complex settings. This theory
complements traditional economic techniques, which generally focus on exact and
optimal solutions and are accordingly limited to relatively stylized settings.
We highlight three user-friendly analytical tools: smoothness-type
inequalities, which immediately yield approximation guarantees for many auction
formats of interest in the special case of complete information and
deterministic strategies; extension theorems, which extend such guarantees to
randomized strategies, no-regret learning outcomes, and incomplete-information
settings; and composition theorems, which extend such guarantees from simpler
to more complex auctions. Combining these tools yields tight worst-case
approximation guarantees for the equilibria of many widely-used auction
formats.

本文提出了一种通用的、模块化的理论来证明竞拍中的平衡近似保证，该理论补充了传统经济技术，着重于精确和最优解决方案，并因此局限于相对简化的设置。我们提出了三个用户友好的分析工具：平滑型不等式、扩展定理和组合定理，将这些工具结合起来，为许多广泛使用的拍卖格式的均衡提供了严格的最坏情况近似保证。