Cover image for Putting auction theory to work
Title:
Putting auction theory to work
Author:
Milgrom, Paul R. (Paul Robert), 1948-
Publication Information:
Cambridge, UK ; New York : Cambridge University Press, 2004.
Physical Description:
xxii, 368 pages : illustrations ; 24 cm.
Language:
English
ISBN:
9780521551847

9780521536721
Format :
Book

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Summary

Summary

This book provides a comprehensive introduction to modern auction theory and its important new applications. It 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 book gives the most up-to-date treatments of both traditional theories of 'optimal auctions' and newer theories of multi-unit auctions and package auctions, and shows by example how these theories are used. The analysis explores the limitations of prominent older designs, such as the Vickrey auction design, and evaluates the practical responses to those limitations. It explores the tension between the traditional theory of auctions with a fixed set of bidders, in which the seller seeks to squeeze as much revenue as possible from the fixed set, and the theory of auctions with endogenous entry, in which bidder profits must be respected to encourage participation.


Table of Contents

Evan Kwerel
Prefacep. xi
Forewordp. xv
1 Getting to Workp. 1
1.1 Politics Sets the Stagep. 3
1.2 Designing for Multiple Goalsp. 3
1.2.1 Substitutes and Complementsp. 6
1.2.2 New Zealand's Rights Auctionp. 9
1.2.3 Better Auction Designsp. 13
1.2.4 The FCC Design and Its Progenyp. 13
1.3 Comparing Seller Revenuesp. 16
1.4 The Academic Criticsp. 19
1.4.1 Resale and the Coase Theoremp. 19
1.4.2 Mechanism Design Theoryp. 21
1.4.3 Theory and Experimentp. 25
1.4.4 Practical Concernsp. 26
1.5 Plan for This Bookp. 31
Part 1 The Mechanism Design Approachp. 35
2 Vickrey-Clarke-Groves Mechanismsp. 45
2.1 Formulationp. 45
2.2 Always Optimal and Weakly Dominant Strategiesp. 49
2.3 Balancing the Budgetp. 53
2.4 Uniquenessp. 55
2.5 Disadvantages of the Vickrey Auctionp. 56
2.5.1 Practical Disadvantagesp. 56
2.5.2 Monotonicity Problemsp. 57
2.5.3 The Merger-Investment Disadvantagep. 60
2.6 Conclusionp. 61
3 The Envelope Theorem and Payoff Equivalencep. 64
3.1 Hotelling's Lemmap. 65
3.2 The Envelope Theorem in Integral Formp. 66
3.3 Quasi-linear Payoffsp. 69
3.3.1 Holmstrom's Lemmap. 70
3.3.2 The Green-Laffont-Holmstrom Theoremp. 71
3.3.3 Myerson's Lemmap. 73
3.3.4 Revenue Equivalence Theoremsp. 75
3.3.5 The Myerson-Satterthwaite Theoremp. 77
3.3.6 The Jehiel-Moldovanu Impossibility Theoremsp. 80
3.3.7 Myerson and Riley-Samuelson Revenue-Maximizing Auctionsp. 84
3.3.8 The McAfee-McMillan Weak-Cartels Theoremp. 87
3.3.9 Sequential Auctions and Weber's Martingale Theoremp. 90
3.3.10 Matthews Theorem: Risk Averse Payoff Equivalencep. 91
3.4 Conclusionp. 94
4 Bidding Equilibrium and Revenue Differencesp. 98
4.1 The Single Crossing Conditionsp. 99
4.1.1 The Monotonic Selection Theoremp. 101
4.1.2 The Sufficiency Theoremp. 102
4.1.3 The Constraint Simplification Theoremp. 105
4.1.4 The Mirrlees-Spence Representation Theoremp. 106
4.2 Deriving and Verifying Equilibrium Strategiesp. 110
4.2.1 The Second-Price Auction with a Reserve Pricep. 111
4.2.2 The Sealed Tender, or First-Price, Auctionp. 112
4.2.3 The War of Attrition Auctionp. 117
4.2.4 The All-Pay Auctionp. 119
4.3 Revenue Comparisons in the Benchmark Modelp. 119
4.3.1 Payoff Equivalence without Revenue Equivalencep. 121
4.3.2 Budget Constraintsp. 132
4.3.3 Endogenous Quantitiesp. 135
4.3.4 Correlated Typesp. 137
4.4 Expected-Revenue-Maximizing Auctionsp. 140
4.4.1 Myerson's Theoremp. 144
4.4.2 Bulow-Klemperer Theoremp. 148
4.4.3 The Irregular Casep. 148
4.5 Auctions with Weak and Strong Biddersp. 149
4.6 Conclusionp. 154
5 Interdependence of Types and Valuesp. 157
5.1 Which Models and Assumptions are "Useful"?p. 158
5.1.1 Payoffs Depend Only on Bids and Typesp. 158
5.1.2 Types Are One-Dimensional and Values Are Privatep. 159
5.1.3 Types Are Statistically Independentp. 161
5.2 Statistical Dependence and Revenue-Maximizing Auctionsp. 162
5.3 Wilson's Drainage Tract Modelp. 166
5.3.1 Equilibriump. 167
5.3.2 Profits and Revenuesp. 173
5.3.3 Bidder Information Policyp. 175
5.3.4 Seller Information Policyp. 177
5.4 Correlated Types and Interdependent Valuesp. 181
5.4.1 Affiliationp. 182
5.4.2 The Milgrom-Weber Ascending Auction Modelsp. 187
5.4.2.1 The (Second-Price) Button Auction with Minimal Informationp. 188
5.4.2.2 The Button Auction with Maximal Informationp. 195
5.4.2.3 Some Revenue Comparisonsp. 198
5.4.3 First-Price Auctionsp. 200
5.5 Conclusionp. 204
6 Auctions in Contextp. 208
6.1 The Profit and Surplus Contribution of an Entrantp. 214
6.2 Symmetric Models with Costly Entryp. 216
6.2.1 Symmetric Bidders and Uncoordinated Entryp. 218
6.2.1.1 Equilibrium in Entry and Bidding Decisionsp. 218
6.2.1.2 Setting the Reserve Pricep. 222
6.2.2 Coordinating Entry among Symmetric Competitorsp. 225
6.2.2.1 Pre-qualifying Biddersp. 227
6.2.2.2 Auctions, Negotiations, and Posted Pricesp. 230
6.2.2.3 Buy Pricesp. 232
6.3 Asymmetric Models: Devices to Promote Competitionp. 234
6.3.1 Example of Set-asidesp. 235
6.3.2 Example of Bidding Creditsp. 237
6.3.3 Example of Lot Structure and Consolation Prizesp. 238
6.3.4 Premium Auctionsp. 239
6.3.5 Dutch vs. English Auctions and the Anglo-Dutch Designp. 241
6.4 After the Bidding Endsp. 243
6.4.1 Bankruptcy and Non-performancep. 243
6.4.2 Scoring Rules vs. Price-Only Bidsp. 245
6.5 Conclusionp. 247
Part II Multi-Unit Auctionsp. 251
7 Uniform Price Auctionsp. 255
7.1 Uniform Price Sealed-Bid Auctionsp. 257
7.1.1 Demand Reductionp. 258
7.1.2 Low-Price Equilibriap. 262
7.2 Simultaneous Ascending Auctionsp. 265
7.2.1 The Simultaneous Ascending Auction and the Walrasian Tatonnementp. 268
7.2.2 Clock Auctionsp. 279
7.2.3 Strategic Incentives in Uniform Price Auctionsp. 284
7.2.3.1 The Basic Clock Auction Modelp. 284
7.2.3.2 The Alternating-Move Clock Auctionp. 287
7.2.3.3 Strategic Incentives with Elastic Supplyp. 290
7.3 Conclusionp. 293
8 Package Auctions and Combinatorial Biddingp. 296
8.1 Vickrey Auctions and the Monotonicity Problemsp. 302
8.1.1 Bidders' Vickrey Payoffs Bound Their Core Payoffsp. 305
8.1.2 Vickrey Auctions and the Entry Puzzlep. 305
8.1.3 When Are Vickrey Outcomes in the Core?p. 307
8.1.4 Substitute Goods and Core Outcomesp. 308
8.1.5 Substitute Goods and Vickrey Outcomesp. 312
8.2 Bernheim-Whinston First-Price Package Auctionsp. 315
8.2.1 Formulationp. 316
8.2.2 Profit-Target Strategiesp. 318
8.2.3 Equilibrium and the Corep. 319
8.3 Ausubel-Milgrom Ascending Proxy Auctionsp. 324
8.3.1 The Proxy Auction with Unlimited Budgetsp. 325
8.3.1.1 Proxy Outcomes Are Core Outcomesp. 326
8.3.1.2 Profit-Target Strategies and Equilibriump. 327
8.3.1.3 The Proxy Auction When Goods Are Substitutesp. 329
8.3.2 The Non-transferable-Utility Proxy Auctionp. 330
8.4 Conclusionp. 333
Bibliographyp. 339
Author Indexp. 347
Subject Indexp. 351