AI 中文总结
研究预算可行采购问题的机制设计，针对买家效用、社会福利等广义目标，提出了最优和近似最优机制，包括无先验和贝叶斯设置下的常数因子近似。
AI 中文摘要
我们研究预算可行采购问题的机制设计，这是一个自然出现的问题：当买家希望从多个战略卖家处采购商品或服务时，每个卖家都有提供服务的成本，买家对每项采购的服务有估值，但受预算约束。与先前专注于买家价值最大化的工作不同，我们针对买家效用（采购服务的价值减去支付）、社会福利（价值减去生产成本）以及两者的推广目标，求解最优和近似最优机制。对于社会福利，我们设计了一个简单的机制，在无先验（最坏情况）设置下获得常数因子近似。由于无先验机制无法为效用提供任何保证，即使对于单个卖家也是如此，我们考虑贝叶斯设置，其中买家对卖家的成本具有分布知识。我们首先提供了一个满足买家预算约束（期望意义下）的效用最优机制，然后展示了如何修改该机制以满足事后预算约束（对于卖家成本的每种实现），同时仍获得接近最优的效用保证。最后，我们将我们的机制推广到其他目标。
英文摘要
We study mechanism design for the budget-feasible procurement problem, a natural problem that arises when a buyer wants to procure goods or services from multiple strategic sellers who each have a cost to provide that service, the buyer has a value for each service procured, but is constrained by a budget. In contrast to prior work, which has focused on buyer value maximization for this problem, we solve for optimal and approximately-optimal mechanisms for the objectives of buyer utility (value of procured services minus payments), welfare (value minus production costs), and generalizations of the two. For welfare, we design a simple mechanism that obtains a constant-factor approximation for the prior-free (worst-case) setting. As prior-free mechanisms fail to provide any guarantee for utility, even for a single seller, we consider Bayesian settings, where the buyer has distributional knowledge over sellers' costs. We first provide a utility-optimal mechanism that satisfies the buyer's budget constraint in expectation, then we show how to modify the mechanism to satisfy the budget constraint ex-post, for every realization of seller costs, while still obtaining near-optimal utility guarantees. Finally, we generalize our mechanisms to other objectives.
CommentsAccepted at the Forty-third International Conference on Machine Learning (ICML 2026). Version 2: Corrected alphabetical author order, changed proofs of Proposition 1 and Lemma 6; Main conclusions unchanged. Version 3: Metadata author order fix
