We study the problem of computing competitive equilibria in the Arctic product-mix auction, originally developed for the Icelandic government for exchanging blocked financial accounts, and more recently proposed by IMF staff for sovereign debt restructuring. From the buyers' perspective, the Arctic auction is equivalent to the quasi-linear Fisher market. However, unlike the standard Fisher model, the seller can express rich supply preferences through explicit supply-side costs and constraints. Despite extensive algorithmic literature on Fisher markets, the seller side has not received much attention, and no polynomial-time algorithm was previously known for computing competitive equilibrium when sellers face nontrivial costs. We examine the natural and expressive regime of separable, stepwise-increasing marginal costs that underlie the above-stated applications. Using polyhedral theory techniques, we first show that rational inputs lead to rational-valued competitive equilibria. Motivated by this result, we develop the first polynomial-time algorithm for this setting based on a non-trivial extension of classic primal-dual balanced-flow techniques for linear Fisher markets. Our work provides a robust computational foundation for auctions with sophisticated preferences, paving the way for flexible and institutionally feasible market designs in global finance.

翻译：我们研究北极产品组合拍卖中计算竞争均衡的问题，该拍卖最初为冰岛政府用于交换冻结金融账户而开发，近期被国际货币基金组织员工提议用于主权债务重组。从买家视角看，北极拍卖等价于准线性费雪市场。然而，与标准费雪模型不同，卖家可通过显式供应侧成本与约束表达丰富的供应偏好。尽管关于费雪市场的算法文献广泛，但卖家侧尚未得到充分关注，且当卖家面临非平凡成本时，此前尚无已知的多项式时间算法用于计算竞争均衡。我们研究上述应用场景中可分离、阶梯递增边际成本的自然且富有表达力的机制。通过多面体理论技术，我们首先证明有理输入会导出有理值的竞争均衡。受此结果启发，我们基于经典线性费雪市场中原始-对偶平衡流技术的非平凡扩展，开发了适用于该场景的首个多项式时间算法。我们的工作为具有复杂偏好的拍卖提供了稳健的计算基础，为全球金融中灵活且制度可行的市场设计铺平了道路。