Our main contribution is a strongly polynomial algorithm for computing an equilibrium for the Arctic Auction, which is the quasi-linear extension of the linear Fisher market model. We build directly on Orlin's strongly polynomial algorithm for the linear Fisher market (Orlin, 2010). The first combinatorial polynomial algorithm for the linear Fisher market was based on the primal-dual paradigm (Devanur et al., 2008). This was followed by Orlin's scaling-based algorithms. The Arctic Auction (Klemperer 2018) was developed for the Government of Iceland to allow individuals to exchange blocked offshore assets. It is a variant of the product-mix auction (Klemperer 2008, 2010, 2018) that was designed for, and used by, the Bank of England, to allocate liquidity efficiently across banks pledging heterogeneous collateral of varying quality. Our work was motivated by the fact that banks often need to run Arctic Auctions under many different settings of the parameters in order to home in on the right one, making it essential to find a time-efficient algorithm for Arctic Auction.

翻译：我们的主要贡献是给出了北极拍卖（Arctic Auction）均衡的一个强多项式算法，该模型是线性Fisher市场模型的拟线性扩展。我们直接基于Orlin针对线性Fisher市场提出的强多项式算法（Orlin, 2010）。线性Fisher市场的首个组合多项式算法基于原始-对偶范式（Devanur等人，2008），随后Orlin提出了基于缩放（scaling）的算法。北极拍卖（Klemperer, 2018）是为冰岛政府设计的，允许个人交换被冻结的离岸资产。它是产品组合拍卖（product-mix auction, Klemperer, 2008, 2010, 2018）的一个变体，后者由英格兰银行设计并实际用于在银行间高效分配流动性，在此过程中银行需质押不同质量的异质性抵押品。我们的工作源于以下实际需求：银行往往需要在多种不同参数设置下反复运行北极拍卖以确定最优参数，因此寻找北极拍卖的高效时间算法至关重要。