We develop a general duality-theory framework for revenue maximization in
additive Bayesian auctions. The framework extends linear programming duality
and complementarity to constraints with partial derivatives. The dual system
reveals the geometric nature of the problem and highlights its connection with
the theory of bipartite graph matchings. We demonstrate the power of the
framework by applying it to a multiple-good monopoly setting where the buyer
has uniformly distributed valuations for the items, the canonical long-standing
open problem in the area. We propose a deterministic selling mechanism called
Straight-Jacket Auction (SJA), which we prove to be exactly optimal for up to 6
items, and conjecture its optimality for any number of goods. The duality
framework is used not only for proving optimality, but perhaps more importantly
for deriving the optimal mechanism itself; as a result, SJA is defined by
natural geometric constraints.

该研究提出了一个通用的二元性理论框架，用于在贝叶斯加法拍卖中实现收入最大化，应用线性规划的二元性和补充性到具有偏导数限制的约束中，将对偶系统用于推导最佳机制，并提出一种叫做 SJA 的确定性销售机制，经证明在最多 6 件物品的情况下是最优的。