发表机构
Tel Aviv University（特拉维夫大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究解决多维机制设计中剩余剩余最大化的最坏情况可近似性问题，提出普遍真实且事后个体理性的机制，得到最优最坏情况保证，解决相关开放问题并改进现有结果。
AI 中文摘要
我们解决了一般多维机制设计环境下剩余剩余最大化的最坏情况可近似性问题。对于在有限结果空间上具有任意非负估值的n个智能体，我们提出了一种普遍真实且事后个体理性的机制，其预期剩余剩余至少为W(N)/H_n，其中W(N)是最优社会福利，H_n是第n个调和数。该保证是最坏情况下最优的，包括其常数项，即使在具有已知独立同分布先验的单物品拍卖中，以及在贝叶斯激励兼容性这一较弱要求下也成立。我们的结果解决了Hartline和Roughgarden（2008）提出的关于金钱焚烧在k单位拍卖之外的作用这一开放问题的福利近似方面，以及Ezra等人（2025）提出的关于更广泛估值类别的最优保证的开放问题。它还以依赖于智能体的紧因子H_n取代了Fotakis等人（2015）提出的依赖于结果的O(log|O|)保证，同时将期望真实性加强为普遍真实性。只要福利最大化VCG是多项式时间的，该机制就是多项式时间的，从而产生针对 gross-substitutes（ gross替代品）和多单元估值以及几种自然单参数可行性约束的高效机制。
英文摘要
We settle the worst-case approximability of consumer-surplus maximization in general multidimensional mechanism-design environments. We do so through two black-box reductions from welfare maximization to the agents' total utility. Our first reduction turns exact welfare maximization into a prior-free, universally truthful and ex-post individually rational mechanism that preserves at least a $1/H_n$ fraction of optimal welfare as expected consumer surplus. The guarantee holds for $n$ agents with arbitrary nonnegative valuations over a finite outcome space, where $H_n$ is the $n$-th harmonic number. The factor $H_n$ is worst-case optimal, including its constant, even for a single-item auction with a known i.i.d. prior and Bayesian incentive compatibility. Our second reduction allows existing truthful welfare approximation mechanisms to be reused for surplus maximization. For valuation classes closed under scaling, it converts any ex-post individually rational, truthful $α$-approximation for welfare with nonnegative payments into an $O(α\log(n))$-approximation for surplus. Our sharp guarantee resolves the welfare-approximation aspect of the open question of Hartline and Roughgarden [2008] on the power of money burning beyond $k$-unit auctions, and the question of Ezra et al. [2025] concerning optimal surplus guarantees for broader valuation classes. It also replaces the outcome-dependent $O(\log|\mathcal{O}|)$ guarantee of Fotakis et al. [2015] with the tight agent-dependent factor $H_n$. These results yield polynomial-time mechanisms with the exact $H_n$ guarantee for gross-substitutes. They also give prior-free, universally truthful approximations of $O(H_n\log^2\log m)$ for XOS valuations and $O(H_n\log^3\log m)$ for subadditive valuations using demand and value queries, where $m$ is the number of items.
