Hurwicz 教授的Designing economic mechanism

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收藏 2008-06-23

Acknowledgements page ix Introduction 1 1 Mechanisms and Mechanism Design 14 1.0 Introduction 14 1.1 Mechanisms and Design 18 1.2 Environments and Goal Functions 25 1.3 Mechanisms: Message Exchange Processes and Game Forms 26 1.4 Initial Dispersion of Information and Privacy Preservation 29 1.5 Mechanism Design 30 1.6 Mechanism Design Illustrated in aWalrasian Example 31 1.6.1 An Edgeworth Box Economy 31 1.6.2 TheWalrasian Goal Function 32 1.6.3 Mechanisms: The Competitive Mechanism 35 1.6.4 Competitive Equilibrium Conditions 35 1.6.5 The Competitive Mechanism Is a Mechanism 36 1.6.6 The Competitive Mechanism Illustrates Some Concepts Used in Mechanism Design 37 1.6.7 Privacy Preservation in the Competitive Mechanism 38 1.6.8 Deriving a Mechanism (Not the Competitive Mechanism) from a Covering for theWalrasian Goal Function 40 1.6.9 Informational Properties of the Two Mechanisms 42 1.6.10 The Rectangles Method Applied to theWalrasian Goal Function – Informal 44 v vi Contents 1.7 Introductory Discussion of Informational Efficiency Concepts 46 1.8 A National Forest 50 2 From Goals to Means: Constructing Mechanisms 63 2.1 Phase One: Mechanism Construction 74 2.1.1 Two Examples 74 2.1.2 Constructing a “Universal” Method of Designing Informationally Efficient Mechanisms Realizing a Given Goal Function 83 2.1.3 The Method of Rectangles (RM) 86 2.2 Phase 2: Constructing Decentralized Mechanisms, from Parameter Indexed Product Structures: Transition to Message-Indexed Product Structures 101 2.2.0 Introduction 101 2.2.1 Basic Concepts 102 2.2.2 The L-dot Example 104 2.2.3 More Examples 105 2.2.4 General Issues in Mechanism Construction 109 2.2.5 Mechanism Construction for L-dot 114 2.3 Smooth Transversal Construction for Partitions by the “Flagpole” Method 117 2.3.1 Flagpoles: General Principles 117 2.3.2 Flagpoles: Example 2 (Augmented Inner Product) 120 2.3.3 Flagpoles: A Walrasian Example 125 2.3.4 Unique Solvability Implies Partition 129 2.4 Analytic Aspects 130 2.4.1 Phase Two via Condensation. General Principles 131 2.4.2 The Mount–Reiter Condensation Theorem (Sufficiency) 136 2.4.3 Walrasian Mechanism Construction 140 2.4.4 Phase Two of Mechanism Design via Condensation for the Augmented Two-Dimensional Inner Product 149 2.5 Overlaps 154 2.5.0 Constructing a Mechanism When the Parameter-Indexed Product Structure Is Not a Partition: An Example 154 Appendix 163 2.6 Informational Efficiency 165 2.6.1 Main Results 165 2.6.2 The Maximality of Reflexive RM-Coverings 166 2.6.3 Informational Efficiency: General Considerations 168 Contents vii 2.6.4 A Comment on Informational Efficiency Concepts 171 2.6.5 Minimal Informational Size Is Achievable by an rRM Mechanism 172 2.6.6 Two rRM Coverings of Different Informational Size for the Same Goal Function: An Example 175 Appendix 180 3 Designing Informationally Efficient Mechanisms Using the Language of Sets 182 3.1 Introduction 182 3.2 Mechanism Design 183 3.2.1 Decentralization 184 3.3 Mechanisms and Coverings 186 3.4 A Systematic Process for Constructing an rRM Covering 188 3.4.1 OrRM: An Algorithm for Constructing an rRM Covering of a Finite Parameter Space That Is Minimal in the Class of Rectangular, F-Contour Contained Coverings 197 3.5 Constructing a Mechanism from a Covering by the Transversals Method (TM) 220 3.6 Coverings and Partitions 230 3.7 Informational Efficiency 244 3.7.1 Introduction 244 3.7.2 Observational Efficiency 245 3.7.3 The Maximality of rRM-Coverings 246 3.7.4 Informational Size and Coarseness 250 3.8 Section 1.8 Revisited: A Graphical Presentation 263 3.9 Strategic Behavior 274 3.9.1 Dominant Strategy Implementation 274 3.9.2 Designing Informationally Efficient Nash-Implementing Mechanisms 279 Appendix: Characterizations of Partitions 290 4 Revelation Mechanisms 296 4.1 Introduction 296 4.1.1 Computational Complexity of Functions 299 4.1.2 Separator Sets and Quotients 303 4.1.3 Algebraic Conditions 306 4.1.4 Privacy-Preserving Mechanisms 307 4.2 Initial Set-Theoretic Constructions 310 4.2.1 Encoded and Essential Revelation Mechanisms 310 4.2.2 F-Equivalence and Encoded Revelation Mechanisms 310 viii Contents 4.3 The Topological Case 313 4.3.1 Differential Separability 315 4.3.2 The Number of Variables on which F Really Depends 316 4.3.3 Rank Conditions and Construction of an Essential Revelation Mechanism for F 317 4.4 Proofs and Examples 322 4.4.1 Leontief and Abelson Theorem 322 4.4.2 Leontief ’s Theorem 324 4.4.3 An Example of the Coordinate Construction 329 4.4.4 Proof of Theorem 4.4.6 331 References 335 Index 341