[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