Algorithmic Mechanism Design Through the lens of Multi-unit auctions

Mechanism Design is a sub-field of game theory that aims to design games whose equilibria have desired properties such as achieving high efficiency or high revenue. Algorithmic Mechanism Design is a subfield that lies on the border of Mechanism Design and Computer Science and deals with Mechanism Design in algorithmically-complex scenarios that are often found in computational settings such as the Internet. The central challenge in Algorithmic Mechanism Design is the tension between the computational constraints and the game-theoretic ones. This survey demonstrates both the tension and ways of addressing it by focusing on a single simple problem: multi-unit auctions. A variety of issues will be discussed: representation, computational hardness, communication, convexity, approximations, VCG mechanisms and their generalizations, single-parameter settings vs. multi-parameter settings, and the power of randomness.