Mechanism Design: A Linear Programming Approach

by Rakesh V. Vohra

Overview

Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design.

Product Details

ISBN-13:	9780521179461
Publisher:	Cambridge University Press
Publication date:	05/09/2011
Series:	Econometric Society Monographs , #47
Edition description:	New Edition
Pages:	184
Product dimensions:	6.00(w) x 8.90(h) x 0.60(d)

About the Author

Rakesh V. Vohra is the John L. and Helen Kellogg Professor of Managerial Economics and Decision Sciences at the Kellogg School of Management, Northwestern University, where he is also Director of the Center for Mathematical Studies in Economics and Management Science. He previously taught at the Fisher School of Business, Ohio State University and is the author of Advanced Mathematical Economics (2005). Professor Vohra has also completed a manuscript on the principles of pricing with Lakshman Krishnamurthi, Professor of Marketing at the Kellogg School. Professor Vohra received his doctorate in mathematics from the University of Maryland.

Table of Contents

1. Introduction; 2. Arrow's theorem and its consequences; 3. Network flow problem; 4. Incentive compatibility; 5. Efficiency; 6. Revenue maximization; 7. Rationalizability.

Editorial Reviews

The new book by Vohra is an excellent and most timely introduction into mechanism design. It offers a concise introduction to the theory of mechanism design, currently missing in the literature; it uses linear programming to great benefit to analyze the structure of incentives; and it provides a comprehensive account of the seminal results in auction and mechanism design. A splendid treatment for advanced undergraduate and graduate courses in economic theory!” – Dirk Bergemann, Yale University

“Rakesh Vohra’s exposition of the theory of mechanism design is wonderfully transparent and elegant. This short book equips the reader with a remarkably deep and comprehensive understanding of this important subject.” – Tilman Borgers, University of Michigan

“Vohra convincingly demonstrates that linear programming can give a powerful and unified perspective on mechanism design, clarifying the ideas and methods underlying existing results, and leading in many cases to greater generality or new findings. Graduate students, researchers in other areas, and experienced mechanism designers will all benefit from this book, which will influence mechanism design research for years to come.” – Andrew McLennan, University of Queensland, Australia

“Professor Vohra’s rigorous text is unique in showing how numerous central results in mechanism design can be unified using the methodology of linear programming. His treatment is elegant and original, and it touches the most recent research frontiers. – Benny Moldovanu, University of Bonn, Germany

“Rakesh Vohra takes the reader from the basics of social choice theory and network flow problems to a deep understanding of optimal incentive systems for complex resource-allocation problems, using the mathematics of linear programming elegantly throughout the book.” – Roger Myerson, 2007 Nobel Laureate, University of Chicago

“By situating the fundamental questions of social choice, incentive compatibility, and auction design within the theory of linear programming, Vohra is able to address the modern themes of mechanism design in a cohesive manner. The result is inspiring, enjoyable, and extremely compelling.” – David Parkes, Harvard University

“This beautiful book provides an insightful and useful treatment of the fundamental theorems of social choice and mechanism design from the unifying and powerful perspective of linear programming. A terrific read covering a broad range of topics including a serious and rare treatment of multidimensional mechanism design.” – Phillip J. Reny, University of Chicago

From the Publisher