Providing a comprehensive introduction to modern auction theory and its important new applications, this book is written by a leading economic theorist whose suggestions guided the creation of the new spectrum auction designs. Aimed at graduate students and professionals in economics, the volume provides the most up-to-date analysis of traditional theories of "optimal auctions" as well as newer theories of multi-unit auctions and package auctions, and shows by example how these theories are used. It explores the limitations of prominent older designs, such as the Vickrey auction design, and evaluates the practical responses to those limitations. Paul Milgrom is the Leonard and Shirley Ely Professor of Humanities and Sciences and Professor of Economics, Stanford University. He is the author of more than sixty articles and co-author of the influential textbook, Economics, Organization and Management (Prentice Hall, 1992). Professor Milgrom is a pioneer in the economic theory of auctions and co-designer of the simultaneous, multiple round auction that the FCC adopted for selling radio spectrum licenses.
Author(s): Paul Milgrom
Series: Churchill Lectures in Economics
Edition: 1
Publisher: Cambridge University Press
Year: 2004
Language: English
Pages: 393
Half-title......Page 2
Title......Page 6
Copyright......Page 7
Table of Contents......Page 8
Preface......Page 12
Foreword......Page 16
CHAPTER ONE: Getting to Work......Page 26
1.2 Designing for Multiple Goals......Page 28
1.2.1 Substitutes and Complements......Page 31
1.2.2 New Zealand's Rights Auction......Page 34
1.2.4 The FCC Design and Its Progeny......Page 38
1.3 Comparing Seller Revenues......Page 41
1.4.1 Resale and the Coase Theorem......Page 44
1.4.2 Mechanism Design Theory......Page 46
1.4.3 Theory and Experiment......Page 50
1.4.4 Practical Concerns......Page 51
1.5 Plan for This Book......Page 56
REFERENCES......Page 58
PART ONE: THE MECHANISM DESIGN APPROACH......Page 60
Formalities of the Mechanism Design Model......Page 64
The Chapters of Part I......Page 67
REFERENCES......Page 68
2.1 Formulation......Page 70
2.2 Always Optimal and Weakly Dominant Strategies......Page 74
2.3 Balancing the Budget......Page 78
2.4 Uniqueness......Page 80
2.5.1 Practical Disadvantages......Page 81
2.5.2 Monotonicity Problems......Page 82
2.5.3 The Merger–Investment Disadvantage......Page 85
2.6 Conclusion......Page 86
REFERENCES......Page 87
CHAPTER THREE: The Envelope Theorem and Payoff Equivalence......Page 89
3.1 Hotelling's Lemma......Page 90
3.2 The Envelope Theorem in Integral Form......Page 91
3.3 Quasi-linear Payoffs......Page 94
3.3.1 Holmstrom's Lemma......Page 95
3.3.2 The Green–Laffont–Holmstrom Theorem......Page 96
3.3.3 Myerson's Lemma......Page 98
3.3.4 Revenue Equivalence Theorems......Page 100
3.3.5 The Myerson–Satterthwaite Theorem......Page 102
3.3.5.1 Application: Auctions Versus Lotteries......Page 104
3.3.6 The Jehiel–Moldovanu Impossibility Theorems......Page 105
Definitions......Page 109
3.3.8 The McAfee–McMillan Weak-Cartels Theorem......Page 112
3.3.9 Sequential Auctions and Weber's Martingale Theorem......Page 115
3.3.10 Matthews' Theorem: Risk Averse Payoff Equivalence......Page 116
3.4 Conclusion......Page 119
REFERENCES......Page 121
CHAPTER FOUR: Bidding Equilibrium and Revenue Differences......Page 123
4.1 The Single Crossing Conditions......Page 124
4.1.1 The Monotonic Selection Theorem......Page 126
4.1.2 The Sufficiency Theorem......Page 127
4.1.3 The Constraint Simplification Theorem......Page 130
4.1.4 The Mirrlees–Spence Representation Theorem......Page 131
4.2 Deriving and Verifying Equilibrium Strategies......Page 135
4.2.1 The Second-Price Auction with a Reserve Price......Page 136
4.2.2 The Sealed Tender, or First-Price, Auction......Page 137
4.2.3 The War of Attrition Auction......Page 142
4.3 Revenue Comparisons in the Benchmark Model......Page 144
Risk Averse Sellers......Page 146
Risk Averse Bidders......Page 147
4.3.2 Budget Constraints......Page 157
4.3.3 Endogenous Quantities......Page 160
4.3.4 Correlated Types......Page 162
4.4 Expected-Revenue-Maximizing Auctions......Page 165
4.4.1 Myerson's Theorem......Page 169
Examples......Page 170
4.4.3 The Irregular Case......Page 173
4.5 Auctions with Weak and Strong Bidders......Page 174
4.6 Conclusion......Page 179
REFERENCES......Page 180
CHAPTER FIVE: Interdependence of Types and Values......Page 182
5.1.1 Payoffs Depend Only on Bids and Types......Page 183
5.1.2 Types Are One-Dimensional and Values Are Private......Page 184
5.1.3 Types Are Statistically Independent......Page 186
5.2 Statistical Dependence and Revenue-Maximizing Auctions......Page 187
5.3 Wilson's Drainage Tract Model......Page 191
5.3.1 Equilibrium......Page 192
5.3.2 Profits and Revenues......Page 198
5.3.3 Bidder Information Policy......Page 200
5.3.4 Seller Information Policy......Page 202
5.4 Correlated Types and Interdependent Values......Page 206
5.4.1 Affiliation......Page 207
5.4.2 The Milgrom–Weber Ascending Auction Models......Page 212
5.4.2.1 The (Second-Price) Button Auction with Minimal Information......Page 213
5.4.2.2 The Button Auction with Maximal Information......Page 220
5.4.2.3 Some Revenue Comparisons......Page 223
5.4.3 First-Price Auctions......Page 225
5.5 Conclusion......Page 229
REFERENCES......Page 231
CHAPTER SIX: Auctions in Context......Page 233
6.1 The Profit and Surplus Contribution of an Entrant......Page 239
6.2 Symmetric Models with Costly Entry......Page 241
6.2.1.1 Equilibrium in Entry and Bidding Decisions......Page 243
6.2.1.2 Setting the Reserve Price......Page 247
6.2.2 Coordinating Entry among Symmetric Competitors......Page 250
6.2.2.1 Pre-qualifying Bidders......Page 252
6.2.2.2 Auctions, Negotiations, and Posted Prices......Page 255
6.2.2.3 Buy Prices......Page 257
6.3 Asymmetric Models: Devices to Promote Competition......Page 259
6.3.1 Example of Set-asides......Page 260
6.3.2 Example of Bidding Credits......Page 262
6.3.3 Example of Lot Structure and Consolation Prizes......Page 263
6.3.4 Premium Auctions......Page 264
6.3.5 Dutch vs. English Auctions and the Anglo-Dutch Design......Page 266
6.4.1 Bankruptcy and Non-performance......Page 268
6.4.2 Scoring Rules vs. Price-Only Bids......Page 270
6.5 Conclusion......Page 272
REFERENCES......Page 274
PART TWO: MULTI-UNIT AUCTIONS......Page 276
REFERENCES......Page 279
CHAPTER SEVEN: Uniform Price Auctions......Page 280
7.1 Uniform Price Sealed-Bid Auctions......Page 282
7.1.1 Demand Reduction......Page 283
7.1.2 Low-Price Equilibria......Page 287
7.2 Simultaneous Ascending Auctions......Page 290
7.2.1 The Simultaneous Ascending Auction and the Walrasian Tatonnement......Page 293
Notation and Definitions......Page 295
7.2.2 Clock Auctions......Page 304
7.2.3.1 The Basic Clock Auction Model......Page 309
7.2.3.2 The Alternating-Move Clock Auction......Page 312
7.2.3.3 Strategic Incentives with Elastic Supply......Page 315
7.3 Conclusion......Page 318
REFERENCES......Page 320
CHAPTER EIGHT: Package Auctions and Combinatorial Bidding......Page 321
8.1 Vickrey Auctions and the Monotonicity Problems......Page 327
8.1.2 Vickrey Auctions and the Entry Puzzle......Page 330
Definitions......Page 331
8.1.3 When Are Vickrey Outcomes in the Core?......Page 332
8.1.4 Substitute Goods and Core Outcomes......Page 333
8.1.5 Substitute Goods and Vickrey Outcomes......Page 337
8.2 Bernheim–Whinston First-Price Package Auctions......Page 340
8.2.1 Formulation......Page 341
8.2.2 Profit-Target Strategies......Page 343
8.2.3 Equilibrium and the Core......Page 344
8.3 Ausubel–Milgrom Ascending Proxy Auctions......Page 349
8.3.1 The Proxy Auction with Unlimited Budgets......Page 350
8.3.1.1 Proxy Outcomes Are Core Outcomes......Page 351
8.3.1.2 Profit-Target Strategies and Equilibrium......Page 352
8.3.1.3 The Proxy Auction When Goods Are Substitutes......Page 354
8.3.2 The Non-transferable-Utility Proxy Auction......Page 355
8.4 Conclusion......Page 358
REFERENCES......Page 360
Bibliography......Page 364
Author Index......Page 372
Subject Index......Page 376
