发表机构
Renmin University of China; Beijing Institute of Technology（中国人民大学; 北京理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对满足DSIC和事后个体理性的多物品拍卖，对两点分布给出最优确定性机制与多项式时间收益算法，证明一般有限支撑分布下的计算难度，并在参数限制下给出精确与近似算法。
AI 中文摘要
我们研究了占优策略激励相容（DSIC）和事后个体理性下收益最大化的多物品拍卖问题。买家具有加法估值，且所有物品价值均来自同一有限分布的独立抽取。对于每一个两点分布以及任意数量的买家和物品，我们给出了一种显式确定性机制，该机制在所有满足上述要求的随机机制中是最优的，同时还给出了一种多项式时间算法来计算最优期望收益。对于一般有限支撑分布，无论是单个买家搭配任意数量物品，还是两个物品搭配任意数量买家，计算精确最优收益都是#P-难的。对于单个买家，我们还证明了计算最优机制的难度。在前期工作的基础上，我们还在不同参数限制下获得了精确和近似算法：当买家数量、物品数量和支撑大小三者中任意两个固定时，可实现精确多项式时间优化；当仅物品数量固定时，存在一种多项式时间近似方案，对于每个固定的0<ε<1，该方案构造的机制期望收益至少达到最优值的1-ε倍。所有这些算法均满足DSIC和事后个体理性。
英文摘要
We study revenue-maximizing multi-item auctions under dominant-strategy incentive compatibility (DSIC) and ex-post individual rationality. Buyers have additive valuations, and all item values are independent draws from a common finite distribution. For every two-point distribution and arbitrary numbers of buyers and items, we give an explicit deterministic mechanism that is optimal among all randomized mechanisms satisfying these requirements, together with a polynomial-time algorithm for computing the optimal expected revenue. For general finite-support distributions, computing the exact optimal revenue is $\#\mathrm P$-hard, both for a single buyer with an arbitrary number of items and for two items with an arbitrary number of buyers. For a single buyer, we also establish hardness of computing an optimal mechanism. Building on prior work, we also obtain exact and approximate algorithms under different parameter restrictions. Exact polynomial-time optimization is possible whenever any two of the buyer count, item count, and support size are fixed. When only the item count is fixed, a polynomial-time approximation scheme constructs a mechanism with expected revenue at least a $1-\varepsilon$ fraction of the optimum for every fixed $0<\varepsilon<1$. All these algorithms satisfy DSIC and ex-post individual rationality.
Comments51 pages, 1 table
