Putting Auction Theory to Work

Cover......Page 1
Half-title......Page 3
Title......Page 7
Copyright......Page 8
Table of Contents......Page 9
Preface......Page 13
Foreword......Page 17
CHAPTER ONE: Getting to Work......Page 27
1.2 Designing for Multiple Goals......Page 29
1.2.1 Substitutes and Complements......Page 32
1.2.2 New Zealand’s Rights Auction......Page 35
1.2.4 The FCC Design and Its Progeny......Page 39
1.3 Comparing Seller Revenues......Page 42
1.4.1 Resale and the Coase Theorem......Page 45
1.4.2 Mechanism Design Theory......Page 47
1.4.3 Theory and Experiment......Page 51
1.4.4 Practical Concerns......Page 52
1.5 Plan for This Book......Page 57
REFERENCES......Page 59
PART ONE: THE MECHANISM DESIGN APPROACH......Page 61
Formalities of the Mechanism Design Model......Page 65
The Chapters of Part I......Page 68
REFERENCES......Page 69
2.1 Formulation......Page 71
2.2 Always Optimal and Weakly Dominant Strategies......Page 75
2.3 Balancing the Budget......Page 79
2.4 Uniqueness......Page 81
2.5.1 Practical Disadvantages......Page 82
2.5.2 Monotonicity Problems......Page 83
2.5.3 The Merger–Investment Disadvantage......Page 86
2.6 Conclusion......Page 87
REFERENCES......Page 88
CHAPTER THREE: The Envelope Theorem and Payoff Equivalence......Page 90
3.1 Hotelling’s Lemma......Page 91
3.2 The Envelope Theorem in Integral Form......Page 92
3.3 Quasi-linear Payoffs......Page 95
3.3.1 Holmstrom’s Lemma......Page 96
3.3.2 The Green–Laffont–Holmstrom Theorem......Page 97
3.3.3 Myerson’s Lemma......Page 99
3.3.4 Revenue Equivalence Theorems......Page 101
3.3.5 The Myerson–Satterthwaite Theorem......Page 103
3.3.5.1 Application: Auctions Versus Lotteries......Page 105
3.3.6 The Jehiel–Moldovanu Impossibility Theorems......Page 106
Definitions......Page 110
3.3.8 The McAfee–McMillan Weak-Cartels Theorem......Page 113
3.3.9 Sequential Auctions and Weber’s Martingale Theorem......Page 116
3.3.10 Matthews’ Theorem: Risk Averse Payoff Equivalence......Page 117
3.4 Conclusion......Page 120
REFERENCES......Page 122
CHAPTER FOUR: Bidding Equilibrium and Revenue Differences......Page 124
4.1 The Single Crossing Conditions......Page 125
4.1.1 The Monotonic Selection Theorem......Page 127
4.1.2 The Sufficiency Theorem......Page 128
4.1.3 The Constraint Simplification Theorem......Page 131
4.1.4 The Mirrlees–Spence Representation Theorem......Page 132
4.2 Deriving and Verifying Equilibrium Strategies......Page 136
4.2.1 The Second-Price Auction with a Reserve Price......Page 137
4.2.2 The Sealed Tender, or First-Price, Auction......Page 138
4.2.3 The War of Attrition Auction......Page 143
4.3 Revenue Comparisons in the Benchmark Model......Page 145
Risk Averse Sellers......Page 147
Risk Averse Bidders......Page 148
4.3.2 Budget Constraints......Page 158
4.3.3 Endogenous Quantities......Page 161
4.3.4 Correlated Types......Page 163
4.4 Expected-Revenue-Maximizing Auctions......Page 166
4.4.1 Myerson’s Theorem......Page 170
Examples......Page 171
4.4.3 The Irregular Case......Page 174
4.5 Auctions with Weak and Strong Bidders......Page 175
4.6 Conclusion......Page 180
REFERENCES......Page 181
CHAPTER FIVE: Interdependence of Types and Values......Page 183
5.1.1 Payoffs Depend Only on Bids and Types......Page 184
5.1.2 Types Are One-Dimensional and Values Are Private......Page 185
5.1.3 Types Are Statistically Independent......Page 187
5.2 Statistical Dependence and Revenue-Maximizing Auctions......Page 188
5.3 Wilson’s Drainage Tract Model......Page 192
5.3.1 Equilibrium......Page 193
5.3.2 Profits and Revenues......Page 199
5.3.3 Bidder Information Policy......Page 201
5.3.4 Seller Information Policy......Page 203
5.4 Correlated Types and Interdependent Values......Page 207
5.4.1 Affiliation......Page 208
5.4.2 The Milgrom–Weber Ascending Auction Models......Page 213
5.4.2.1 The (Second-Price) Button Auction with Minimal Information......Page 214
5.4.2.2 The Button Auction with Maximal Information......Page 221
5.4.2.3 Some Revenue Comparisons......Page 224
5.4.3 First-Price Auctions......Page 226
5.5 Conclusion......Page 230
REFERENCES......Page 232
CHAPTER SIX: Auctions in Context......Page 234
6.1 The Profit and Surplus Contribution of an Entrant......Page 240
6.2 Symmetric Models with Costly Entry......Page 242
6.2.1.1 Equilibrium in Entry and Bidding Decisions......Page 244
6.2.1.2 Setting the Reserve Price......Page 248
6.2.2 Coordinating Entry among Symmetric Competitors......Page 251
6.2.2.1 Pre-qualifying Bidders......Page 253
6.2.2.2 Auctions, Negotiations, and Posted Prices......Page 256
6.2.2.3 Buy Prices......Page 258
6.3 Asymmetric Models: Devices to Promote Competition......Page 260
6.3.1 Example of Set-asides......Page 261
6.3.2 Example of Bidding Credits......Page 263
6.3.3 Example of Lot Structure and Consolation Prizes......Page 264
6.3.4 Premium Auctions......Page 265
6.3.5 Dutch vs. English Auctions and the Anglo-Dutch Design......Page 267
6.4.1 Bankruptcy and Non-performance......Page 269
6.4.2 Scoring Rules vs. Price-Only Bids......Page 271
6.5 Conclusion......Page 273
REFERENCES......Page 275
PART TWO: MULTI-UNIT AUCTIONS......Page 277
REFERENCES......Page 280
CHAPTER SEVEN: Uniform Price Auctions......Page 281
7.1 Uniform Price Sealed-Bid Auctions......Page 283
7.1.1 Demand Reduction......Page 284
7.1.2 Low-Price Equilibria......Page 288
7.2 Simultaneous Ascending Auctions......Page 291
7.2.1 The Simultaneous Ascending Auction and the Walrasian Tatonnement......Page 294
Notation and Definitions......Page 296
7.2.2 Clock Auctions......Page 305
7.2.3.1 The Basic Clock Auction Model......Page 310
7.2.3.2 The Alternating-Move Clock Auction......Page 313
7.2.3.3 Strategic Incentives with Elastic Supply......Page 316
7.3 Conclusion......Page 319
REFERENCES......Page 321
CHAPTER EIGHT: Package Auctions and Combinatorial Bidding......Page 322
8.1 Vickrey Auctions and the Monotonicity Problems......Page 328
8.1.2 Vickrey Auctions and the Entry Puzzle......Page 331
Definitions......Page 332
8.1.3 When Are Vickrey Outcomes in the Core?......Page 333
8.1.4 Substitute Goods and Core Outcomes......Page 334
8.1.5 Substitute Goods and Vickrey Outcomes......Page 338
8.2 Bernheim–Whinston First-Price Package Auctions......Page 341
8.2.1 Formulation......Page 342
8.2.2 Profit-Target Strategies......Page 344
8.2.3 Equilibrium and the Core......Page 345
8.3 Ausubel–Milgrom Ascending Proxy Auctions......Page 350
8.3.1 The Proxy Auction with Unlimited Budgets......Page 351
8.3.1.1 Proxy Outcomes Are Core Outcomes......Page 352
8.3.1.2 Profit-Target Strategies and Equilibrium......Page 353
8.3.1.3 The Proxy Auction When Goods Are Substitutes......Page 355
8.3.2 The Non-transferable-Utility Proxy Auction......Page 356
8.4 Conclusion......Page 359
REFERENCES......Page 361
Bibliography......Page 365
Author Index......Page 373
Subject Index......Page 377