Pricing in Combinatorial Exchanges

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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.