发表机构
University of Oxford; King’s College London（牛津大学; 伦敦国王学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对北极产品组合拍卖，提出首个强多项式算法求解竞争均衡，通过归约到无成本拍卖及线性市场，并证明均衡价格唯一性。
AI 中文摘要
北极产品组合拍卖允许预算受限的投标人对多种替代商品表达偏好。当拍卖人具有可分离凸分段线性成本时，我们给出了首个强多项式算法来寻找竞争均衡。该算法将强多项式归约到无成本北极拍卖，并结合了现有的无成本北极拍卖强多项式算法。我们还给出了从无成本北极拍卖到线性Fisher市场的多项式时间图灵归约，以及到线性Arrow-Debreu交换市场的强多项式多对一归约。如果一种商品在两个竞争均衡中以正数量售出，则其价格在两个均衡中相同。
英文摘要
Arctic product-mix auctions allow budget-constrained bidders to express preferences over multiple substitute goods. We give the first strongly polynomial algorithm to find the competitive equilibria when the auctioneer has separable convex piecewise-linear costs. It combines a strongly polynomial reduction to the costless Arctic auction with an existing strongly polynomial algorithm for costless Arctic auctions. We also give a polynomial-time Turing reduction from costless Arctic auctions to linear Fisher markets, and a strongly polynomial many-to-one reduction to linear Arrow-Debreu exchange markets. If a good is sold in positive quantity in two competitive equilibria, its price is the same in both.
