AI 中文总结
该研究推进预算可行机制设计，针对次可加估值等提出多项式时间常数近似机制，解决长期开放问题，还为多获胜者选举提供了相关进展。
AI 中文摘要
预算可行机制设计是Singer提出的经典框架，但现有上界与下界之间仍存在较大差距。本文显著推进了该领域的研究现状。首先，在无计算约束的情况下，我们证明存在预算可行的通用真实机制，其近似比为：单调次模估值为3，非单调次模估值为e+1，分别优于之前的3.798和9.742；XOS估值为e+1，优于之前的28；在大规模市场中，该近似比可确定性提升至e；次可加估值为2e+1，优于之前的33，在大规模市场中可确定性提升至2e。此外，对于次可加估值，我们获得了一种运行于多项式时间、使用需求查询的常数近似机制，其优于之前最优的O(log log n)近似，解决了可追溯至Dobzinski、Papadimitriou和Singer的长期开放问题，该学者曾猜想常数近似需要指数级的需求查询。我们通过一种基于非真实间接机制的简单统一框架——近期提出的补偿设计——获得了这些结果。具体而言，我们通过势论证，建立了基于边际贡献支付规则的补偿设计的稳定价格常数界，随后将其转化为真实直接机制。对于次可加估值，论证的核心是一个新的平滑引理，表明每个次可加函数可被自界函数以2倍因子近似，这也具有独立意义，通过证明即使在次可加估值下也存在2e近似核心，轻松解决了多获胜者选举中的一个开放问题。
英文摘要
Budget-feasible mechanism design is a classic framework introduced by Singer, but there is still a wide gap between existing upper and lower bounds. In this paper, we significantly advance the state of the art. First, without computational constraints, we show that there exists a universally truthful budget-feasible mechanism with the following approximation ratios: - $3$ for monotone submodular valuations and $e+1$ for nonmonotone submodular valuations, improving over $3.798$ and $9.742$, respectively. - $e+1$ for XOS valuations, improving over $28$. In large markets, our approximation can be improved deterministically to $e$. - $2e+1$ for subadditive valuations, improving over $33$. In large markets, our approximation can be improved deterministically to $2e$. Moreover, for subadditive valuations, we obtain a constant-approximation mechanism that runs in polynomial time using demand queries. This improves over the previous best approximation of $O(\log \log n)$, resolving a long-standing open problem going back to Dobzinski, Papadimitriou, and Singer, who conjectured that a constant approximation requires exponentially many demand queries. We obtain these results through a simple and unifying framework based on non-truthful indirect mechanisms, recently coined compensation design. In particular, through a potential argument, we establish constant price-of-stability bounds for compensation design based on marginal-contribution payment rules, which we then translate into truthful direct mechanisms. For subadditive valuations, the core of the argument is a new smoothing lemma showing that every subadditive function can be approximated within a factor of $2$ by a self-bounding function. This is also of independent interest, readily addressing an open question in multiwinner elections by showing the existence of a $2e$-approximate core even under subadditive valuations.
CommentsV2 makes a minor correction
