[local]1[/local]伊利诺斯大学Steven R. Williams 教授
COMMUNICATION IN MECHANISM DESIGN——a differential approach
Preface page xi
Acknowledgment xiii
1 Introduction 1
1.1 The Model of a Mechanism 1
1.1.1 Example: The Competitive Mechanism 6
1.1.2 Example: Mechanisms and Noncooperative Solution
Concepts 8
1.2 Encoding and Product Structure 13
1.2.1 Product Structure and Noncooperative Solution
Concepts 16
1.2.2 Example: The Efficient Level of a Public Good 18
1.3 A Theme in Differential Equations 24
1.3.1 Example: Does a Given Mapping Represent Inverse
Demand? 25
1.4 Investigating Mechanisms Using Calculus 27
1.4.1 Example: Selecting the Efficient Level of a Public Good
for Restricted Valuation Functions 30
1.5 Overview of Text 34
2 Classical Concepts and Results 35
2.1 Distribution, Foliation, and Mapping 35
2.1.1 Example: A Discontinuous Distribution D forWhich
the Equivalence in Figure 1.4 Holds 37
2.2 Integrability 38
2.2.1 Example: Integrability and the Equality ofMixed Partials 40
vii
2.3 A Geometric Interpretation of Integrability 42
2.3.1 Example: Integrable and Nonintegrable Distributions 43
2.4 The Frobenius Theorem 48
2.5 The Proof of the Frobenius Theorem 52
2.5.1 The Case of c = 1 and d =2 52
2.5.2 The General Case 54
2.6 Obstacles to Global Equivalence 57



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