This paper studies a joint design problem where a seller can design both the signal structures for the agents to learn their values, and the allocation and payment rules for selling the item. In his seminal work, Myerson (1981) shows how to design the optimal auction with exogenous signals. We show that the problem becomes NP-hard when the seller also has the ability to design the signal structures. Our main result is a polynomial-time approximation scheme (PTAS) for computing the optimal joint design with at most an $\epsilon$ multiplicative loss in expected revenue. Moreover, we show that in our joint design problem, the seller can significantly reduce the information rent of the agents by providing partial information, which ensures a revenue that is at least $1 - \frac{1}{e}$ of the optimal welfare for all valuation distributions.

翻译：本文研究一个联合设计问题，其中卖家既能设计代理了解自身价值的信号结构，也能设计物品的分配与支付规则。在其开创性工作中，Myerson (1981) 展示了如何设计具有外生信号的最优拍卖。我们证明，当卖家同时拥有设计信号结构的能力时，该问题变为NP难问题。我们的主要成果是一个多项式时间近似方案（PTAS），用于计算期望收益最多损失$\epsilon$倍数的最优联合设计。此外，我们证明在该联合设计问题中，卖家通过提供部分信息可显著降低代理的信息租金，从而保证对于所有估值分布至少达到最优社会福利$1 - \frac{1}{e}$的收益。