Pricing in Combinatorial Exchanges

组合拍卖近年来引起了学术界的极大兴趣。除了它们对市场设计的理论重要性外，它们还在频谱许可证的销售、物流和工业采购中得到了应用。然而，该理论几乎只关注单边效应。如今，许多电子市场可以组织成一个组合交易所，允许多个买家和卖家提交一揽子出价。日前电力市场是此类市场的一个典型例子，人们对此类市场的了解要少得多。我们计划研究组合交易所的不同定价形式。在第一个工作包中，我们分析了在日前电力市场上使用的线性价格和匿名价格。我们希望通过分析模型和数值实验来了解这种价格所导致的效率损失。在第二个工作包中，我们研究了非线性和个性化价格，当它们是竞争均衡时，以及当结果是核心时。核心是联合博弈论中的中心解概念，描述了这种市场的稳定解。不幸的是，这样的核心解决方案并不总是存在于组合交换中。我们想研究什么时候拍卖的核心是空的，在数值实验的基础上，并表征价值函数，当这种情况下。此外，我们要考虑买家的预算限制。这些约束在该领域很重要，但它们会导致显著的计算复杂性，因为分配问题不再独立于定价问题。我们希望研究预算约束下分配和定价问题的复杂性，并提出有效的算法来计算这些市场中的价格。我们的总体目标是为组合交易开发一种定价理论。

Combinatorial auctions have attracted substantial academic interest inthe recent years. Apart from their theoretical importance for market design, theyhave found application for the sale of spectrum licenses, in logistics, and in industrialprocurement. However, the theory focuses almost exclusively on single-sidedauctions. Many electronic market places nowadays can be organized as a combinatorialexchange, featuring multiple buyers and sellers who are allowed to submitpackage bids. Day-ahead electricity markets are a prime example of such markets,which are a lot less well understood. We plan to study dierent forms of pricingon combinatorial exchanges. In a rst work package, we analyze linear and anonymousprices as they are being used on day-ahead electricity markets. We want tounderstand the efficiency losses incurred by such prices in analytical models andnumerical experiments. In a second work package, we study non-linear and personalizedprices, when they are a competitive equilibrium, and when outcomes are inthe core. The core is a central solution concept in coalitional game theory, describinga stable solution for such markets. Unfortunately, such a core solution doesnot always exist in combinatorial exchanges. We want to study when the core ofthe auction is empty in numerical experiments based and characterize value functions,when this is the case. In addition, we want to consider budget constraints ofbuyers. Such constraints are important in the eld, but they can lead to signicantcomputational complexity as the allocation problem is not independent from thepricing problem anymore. We want to study the complexity of allocation and pricingproblems with budget constraints and propose effiective algorithms to computeprices in such markets. Our overall goal is the development of a pricing theory forcombinatorial exchanges.