ROBUST MECHANISM DESIGNPDF电子书下载

Robust Mechanism Design： An Introduction 1

1 Introduction 1

2 Leading Example： Allocating a Private Good with Interdependent Values 4

3 Type Spaces 7

4 Robust Foundations for Dominant and Ex Post Incentive Compatibility 15

5 Full Implementation 21

5.1 Ex Post Implementation 22

5.2 Robust Implementation in the Direct Mechanism 23

5.3 The Robustness of Robust Implementation 32

5.4 Robust Implementation in the General Mechanism 33

5.5 Rationalizable Implementation 34

5.6 The Role of the Common Prior 36

5.7 Dynamic Mechanisms 37

5.8 Virtual Implementation 38

6 Open Issues 42

References 43

Chapter 1 Robust Mechanism Design 49

1 Introduction 50

2 Setup 54

2.1 Payoff Environment 54

2.2 Type Spaces 55

2.3 Solution Concepts 56

2.4 Questions 58

2.5 Implicit versus Explicit Modelling of Higher Order Uncertainty and the Universal Type Space 59

3 Examples 62

3.1 F is Interim Implementable on All Type Spaces But not Ex Post Implementable 63

3.2 F is Interim Implementable on All Payoff Type Spaces But not Interim Implementable on All Type Spaces 67

4 Separable Environments 72

4.1 Separable Environments 73

4.2 Full Support Conditions 77

5 The Quasilinear Environment with Budget Balance 81

6 Discussion 90

6.1 A Classical Debate 90

6.2 Genericity 92

6.3 Augmented Ex Post Equivalence 92

References 93

Chapter 2 Ex Post Implementation 97

1 Introduction 97

2 Model 103

3 Monotonicity 105

3.1 Ex Post Monotonicity 105

3.2 Maskin Monotonicity 107

3.3 Public Good Example 109

4 Ex Post Implementation 111

4.1 Necessary Conditions 112

4.2 Sufficient Conditions in Economic Environments 114

4.3 Sufficiency Conditions in Non-economic Environments 117

5 Single Crossing Environment 121

6 Direct Mechanisms 126

7 Single Unit Auction 129

7.1 Model 130

7.2 Monotonicity and the VCG Mechanism 130

7.3 Private Versus Interdependent Values 135

8 Social Choice Sets 137

8.1 Pareto Correspondence 137

8.2 Functions， Sets and Correspondences 141

9 Mixed Strategy Implementation 142

10 Conclusion 147

Appendix A 148

A.1.Private values 148

A.2.Ex post monotonicity no veto for sets 148

References 150

Chapter 3 Robust Implementation in Direct Mechanisms 153

1 Introduction 154

2 Setup 159

3 A Public Good Example 161

4 Robust Implementation 164

5 Necessity of Contraction Property 170

6 The Linear Model 175

7 Single Unit Auction 178

8 Discussion 179

8.1 Dimensionality and Aggregation 179

8.2 Relation to Partial and Ex Post Implementation 183

8.3 Robust and Virtual Implementation in General Environments 183

8.4 Social Choice Correspondences and Sets 185

8.5 The Common Prior Assumption and Strategic Substitutes/ Complements 186

8.6 Informational Foundation of Interdependence 187

9 Appendix 187

References 192

Chapter 4 Robust Implementation in General Mechanisms 195

1 Introduction 195

2 Setup 200

2.1 The Payoff Environment 200

2.2 Type Spaces 201

2.3 Mechanisms 201

2.4 Solution Concepts 201

2.5 Implementation 204

3 Finite Mechanisms 206

3.1 Ex Post Incentive Compatibility 207

3.2 Robust Monotonicity 208

3.3 Robust Measurability 212

3.4 Single Crossing Aggregator Environments 214

3.5 Robust Virtual Implementation 216

3.6 A Coordination Example 216

4 Rationalizable and Robust Implementation in Infinite Mechanisms 218

4.1 Best Response 218

4.2 Material Implementation 221

5 Infinite Mechanisms 223

6 Extensions， Variations and Discussion 230

6.1 Lotteries， Pure Strategies and Bayesian Implementation 230

6.2 Ex Post and Robust Implementation 232

6.3 Extensions 234

7 Appendix 234

7.1 Robust Monotonicity and Dual Robust Monotonicity 234

7.2 A Badly Behaved Mechanism 235

7.3 Coordination Example Continued 236

References 238

Chapter 5 The Role of the Common Prior in Robust Implementation 241

1 Introduction 241

2 Setup 243

3 A Public Good Example 245

4 Discussion 249

References 250

Chapter 6 An Ascending Auction for Interdependent Values： Uniqueness and Robustness to Strategic Uncertainty 253

1 Model 255

2 Static Auction 256

3 Dynamic Auction 258

4 Discussion 260

5 Conclusion 261

References 262

Chapter 7 Robust Virtual Implementation 263

1 Introduction 264

2 Setting 270

2.1 Environment 270

2.2 Mechanisms and Solution Concept 271

2.3 Separability 272

3 An Environment with Interdependent Values for a Single Good 274

4 Strategic Distinguishability 277

4.1 Main Result 277

4.2 The Maximally Revealing Mechanism 279

4.2.1 A class of maximally revealing mechanisms 279

4.2.2 Characterizing rationalizable behavior for small ε 280

4.3 Constructing a Rich Enough Test Set 285

5 Robust Virtual Implementation 286

5.1 Definitions 286

5.2 Necessity 287

5.3 Sufficiency 289

6 Discussion 293

6.1 Abreu-Matsushima Measurability 293

6.2 Interdependence and Pairwise Separability 295

6.3 Intermediate Robustness Notions 296

6.4 Rationalizability and All Equilibria on All Type Spaces 298

6.5 Iterated Deletion of Weakly Dominated Strategies 299

6.6 Implementation in a Direct Mechanism 301

6.7 Exact Implementation and Integer Games 302

7 Appendix 303

References 315

Chapter 8 Multidimensional Private Value Auctions 319

1 Introduction 319

2 The Model 324

3 Seller’s Expected Revenue 326

3.1 Second-Price Auction 326

3.2 First-Price Auction 327

3.3 Revenue Non-Equivalence 328

4 Efficiency 331

5 Equilibrium Existence 333

6 Discussion： Revenue and Information Acquisition 334

6.1 Revenue 334

6.2 Information Acquisition 336

7 Conclusion 339

Appendix A…Proofs 340

Appendix B 353

References 354

Chapter 9 The Robustness of Robust Implementation 357

1 Introduction 357

1.1 Literature 359

2 Setup 360

3 Baseline payoff environments 362

3.1 Approximate Common Knowledge 362

3.2 Payoff Environment Solution Concept 363

3.3 One-Dimensional， Contractive， Supermodular PayoffType Environments 364

4 Main Result 366

5 Discussion 368

Appendix A 369

References 372

Chapter 10 Rationalizable Implementation 375

1 Introduction 375

2 Setup 377

3 Main Result 380

4 The Non-Responsive Case 391

5 Concluding Remarks 397

References 403

Chapter 11 Pricing without Priors 405

1 Introduction 405

2 Model 408

3 Pricing Without Priors 410

4 Discussion 413

References 415

Chapter 12 Robust Monopoly Pricing 417

1 Introduction 417

2 Model 421

3 Maximin Utility 425

4 Minimax Regret 428

5 Discussion 434

Appendix A 436

References 440

Author Index 443

Subject Index 447