"The goal of this proposal is to study the theoretical foundations of computationally efficient large markets. Market Design is a task that is traditionally carried out by economists and game theorists. However, as markets are becoming larger one must take into account computational considerations as well. The field that integrates methodologies from classic mechanism design and computer science is called Algorithmic Mechanism Design.Specifically, Game Theory and Mechanism Design study how selfish players interact. A traditional example is an auction for a single item, where mechanism design studies how to achieve a certain goal, e.g., social welfare or revenue maximization. However, when there are multiple heterogeneous items that may exhibit complementarities and substitutabilities, designing mechanisms becomes much more challenging. While classic mechanism design does offer some solutions, these solutions usually do not scale well, as they are not computationally efficient. The goal of this proposal is to understand whether this gap can be bridged.Most research in Algorithmic Mechanism Design focuses on dominant-strategy auctions, where every bidder always has a bid that is at least as good as any other possible bid. This proposal has two related objectives: (1) prove that in some settings there are no computationally efficient dominant-strategy mechanisms, and (2) develop techniques that will allow characterizing the set of dominant-strategy mechanisms in important auction domains, and design new families of dominant-strategy mechanisms.The proposal is expected to advance the state of the art in problems that are at the heart of Algorithmic Mechanism Design (and, more generally, at the heart of Algorithmic Game Theory)."