Written Preliminary Examination II VCG Redistribution Mechanisms

Mechanism design, originally a subfield of microeconomics that concerns implementing systemic good solutions to problems that involve multiple self-interested agents so as to align their incentives with the objectives of the system designer, is now becoming a standard tool in computer science as more and more computer-related systems and phenomena are understood as interactions between self-interested agents and examined through the lens of economics. A classic result in mechanism design is the well-know VCG mechanism that is efficient, strategyproof, individual rational and runs no deficit. While the VCG mechanism generates high revenue in many settings and is thus highly desired because of it, there are other scenarios where it is desirable to minimize such revenue so as to maximizes the agents’ collective welfare. Although strict budget-balance (i.e. zero VCG revenue) is shown to be impossible to achieve if the other desirable properties of the VCG mechanism are to be maintained [16, 8, 18]. Recent advances, notably a majority of which are from the computer science community [1, 19, 7, 20, 6, 3, 10, 17, 11, 12, 13, 14], demonstrate that a significant fraction of the VCG revenue can be redistributed back to the agents in various settings. In this report, we review three such mechanisms, i.e. the Bailey-Cavallo mechanism [1, 3], the Guo-Conitzer-Moulin mechanism [10, 17], and the optimal-in-expectation linear (OEL) mechanism [12] in a setting called multi-unit single-demand auction, where a set of n agents are interested in allocating m < n identical items among themselves in a way that maximizes their collective welfare. To put things in context, we also give a review of the basic concepts of mechanism design and the VCG mechanism.