Designing Economic Mechanisms / Edition 1

Designing Economic Mechanisms / Edition 1

by Leonid Hurwicz, Stanley Reiter
     
 

ISBN-10: 0521836417

ISBN-13: 9780521836418

Pub. Date: 05/31/2006

Publisher: Cambridge University Press


About the Author:
Leonid Hurwicz is Regents' Professor of Economics Emeritus at the University of Minnesota. Internationally renowned for his pioneering research on economic theory, particularly in the areas of mechanism and institutional design and mathematical economics, he received the National Medal of Science in 1990 and The Nobel Memorial Prize

Overview


About the Author:
Leonid Hurwicz is Regents' Professor of Economics Emeritus at the University of Minnesota. Internationally renowned for his pioneering research on economic theory, particularly in the areas of mechanism and institutional design and mathematical economics, he received the National Medal of Science in 1990 and The Nobel Memorial Prize in Economic Science in 2007

About the Author:
Stanley Reiter is Morrison Professor of Economics and Mathematics in the Weinburg College of Arts and Sciences and Morrison Professor of Managerial Economics and Decision Sciences in the Kellogg School of Management, Northwestern University, where he directs the Center for Mathematical Studies in Economics and Management Science

Product Details

ISBN-13:
9780521836418
Publisher:
Cambridge University Press
Publication date:
05/31/2006
Edition description:
New Edition
Pages:
354
Product dimensions:
5.98(w) x 8.98(h) x 0.98(d)

Table of Contents


Acknowledgements     ix
Introduction     1
Mechanisms and Mechanism Design     14
Introduction     14
Mechanisms and Design     18
Environments and Goal Functions     25
Mechanisms: Message Exchange Processes and Game Forms     26
Initial Dispersion of Information and Privacy Preservation     29
Mechanism Design     30
Mechanism Design Illustrated in a Walrasian Example     31
An Edgeworth Box Economy     31
The Walrasian Goal Function     32
Mechanisms: The Competitive Mechanism     35
Competitive Equilibrium Conditions     35
The Competitive Mechanism Is a Mechanism     36
The Competitive Mechanism Illustrates Some Concepts Used in Mechanism Design     37
Privacy Preservation in the Competitive Mechanism     38
Deriving a Mechanism (Not the Competitive Mechanism) from a Covering for the Walrasian Goal Function     40
Informational Properties of the Two Mechanisms     42
The Rectangles Method Applied to the Walrasian Goal Function-Informal     44
Introductory Discussion of Informational Efficiency Concepts     46
A National Forest     50
From Goals to Means: ConstructingMechanisms     63
Phase One: Mechanism Construction     74
Two Examples     74
Constructing a "Universal" Method of Designing Informationally Efficient Mechanisms Realizing a Given Goal Function     83
The Method of Rectangles (RM)     86
Phase 2: Constructing Decentralized Mechanisms, from Parameter Indexed Product Structures: Transition to Message-Indexed Product Structures     101
Introduction     101
Basic Concepts     102
The L-dot Example     104
More Examples     105
General Issues in Mechanism Construction     109
Mechanism Construction for L-dot     114
Smooth Transversal Construction for Partitions by the "Flagpole" Method     117
Flagpoles: General Principles     117
Flagpoles: Example 2 (Augmented Inner Product)     120
Flagpoles: A Walrasian Example     125
Unique Solvability Implies Partition     129
Analytic Aspects     130
Phase Two via Condensation. General Principles     131
The Mount-Reiter Condensation Theorem (Sufficiency)     136
Walrasian Mechanism Construction     140
Phase Two of Mechanism Design via Condensation for the Augmented Two-Dimensional Inner Product      149
Overlaps     154
Constructing a Mechanism When the Parameter-Indexed Product Structure Is Not a Partition: An Example     154
Appendix     163
Informational Efficiency     165
Main Results     165
The Maximality of Reflexive RM-Coverings     166
Informational Efficiency: General Considerations     168
A Comment on Informational Efficiency Concepts     171
Minimal Informational Size Is Achievable by an rRM Mechanism     172
Two rRM Coverings of Different Informational Size for the Same Goal Function: An Example     175
Appendix     180
Designing Informationally Efficient Mechanisms Using the Language of Sets     182
Introduction     182
Mechanism Design     183
Decentralization     184
Mechanisms and Coverings     186
A Systematic Process for Constructing an rRM Covering     188
OrRM: An Algorithm for Constructing an rRM Covering of a Finite Parameter Space That Is Minimal in the Class of Rectangular, F-Contour Contianed Coverings     197
Constructing a Mechanism from a Covering by the Transversals Method (TM)     220
Coverings and Partitions     230
Informational Efficiency     244
Introduction      244
Observational Efficiency     245
The Maximality of rRM-Coverings     246
Informational Size and Coarseness     250
Section 1.8 Revisited: A Graphical Presentation     263
Strategic Behavior     274
Dominant Strategy Implementation     274
Designing Informationally Efficient Nash-Implementing Mechanisms     279
Characterizations of Partitions     290
Revelation Mechanisms     296
Introduction     296
Computational Complexity of Functions     299
Separator Sets and Quotients     303
Algebraic Conditions     306
Privacy-Preserving Mechanisms     307
Initial Set-Theoretic Constructions     310
Encoded and Essential Revelation Mechanisms     310
F-Equivalence and Encoded Revelation Mechanisms     310
The Topological Case     313
Differential Separability     315
The Number of Variables on which F Really Depends     316
Rank Conditions and Construction of an Essential Revelation Mechanism for F     317
Proofs and Examples     322
Leontief and Abelson Theorem     322
Leontief's Theorem     324
An Example of the Coordinate Construction     329
Proof of Theorem 4.4.6     331
References     335
Index     341

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