Dynamic Pricing Schemes in Combinatorial Markets

Abstract

In combinatorial markets where buyers are self-interested, the buyers may make purchases that lead to suboptimal item allocations. As a central coordinator, our goal is to impose prices on the items of the market so that its buyers are incentivized to exclusively make optimal purchases. In this thesis, we study the question of whether dynamic pricing schemes can achieve the optimal social welfare in multi-demand combinatorial markets. This well-motivated question has been the topic of some study, but has remained mostly open, and to date, positive results are only known for extremal cases.

In this thesis, we present the current results for unit-demand, bi-demand and tri-demand markets. In the context of these results, we discuss the significance of not having a deficiency of items, which is known as the (OPT) condition. We outline an approach for handling an item deficiency, and we expose barriers to extending the known techniques to markets of larger demand.