An Introduction to Auction Theory

by Menezes, Flavio M.; Monteiro, Paulo K.

• ISBN13: 9780199275991
• ISBN10: 0199275998
• eBook ISBN(s): 9780191534720
• Format: Paperback
• Copyright: 2008-08-26
• Publisher: Oxford University Press
• More Book Details

Summary

The practical importance of auction theory is widely recognized. Indeed, economists have been recognized for their contribution to the design of several auction-like mechanisms, such as the U. S. Federal Communications Commission spectrum auctions, the 3G auctions in Europe and beyond, and the auction markets for electricity markets around the world. Moreover, auction theory is now seen as an important component of an economist's training. For example, some of the more celebrated results from the single-object auction theory are now usually taught in advanced undergraduate and first-year graduate courses on the economics of information. The techniques and insights gained from the study of auction theory provide a useful starting point for those who want to venture into the economics of information, mechanism design, and regulatory economics. This book provides a step-by-step, self-contained treatment of the theory of auctions. The aim is to provide an introductory textbook that will allow students and readers with a calculus background to work through all the basic results. Coverage includes: the basic independent-private-model; the effects of introducing correlation in valuations on equilibrium behaviour and the seller's expected revenue; mechanism design; and the theory of multi-object auctions. The paperback edition of the text includes a new chapter which acts as a guide to current developments in auction theory.

Author Biography

Flavio Menezes joined the University of Queensland as a Chair in Economics after more than a decade at the Australian National University, where he was, amongst other responsibilities, the Foundation Director of the Australian Centre of Regulatory Economics. Flavio is also a former part-time Vice President and Senior Consultant with the Regulatory Economics and Public Policy Practice at CRA International in Canberra. Flavio Menezes has published widely in the economics of information and uncertainty. He is regarded as Australasia's leading auction expert. Paulo Monteiro was Associate Professor at Federal University of Rio de Janeiro and then at IMPA (Institute of Pure and Applied Mathematics.) He is presently at the Postgraduate School of Economics of the Getulio Vargas Foundation (FGV-EPGE). Monteiro researches on infinite dimensional general equilibrium theory, mechanism design, and auction theory.

Table of Contents

Introduction	p. 1
Preliminaries	p. 5
Notation	p. 5
Bayesian Nash Equilibrium	p. 6
Auctions as Games	p. 9
What is an Auction?	p. 9
Auction Types	p. 10
Auction as Bayesian Games	p. 11
Private Values	p. 13
The Independent Private Values Model	p. 13
First-price Auctions	p. 14
Second-price Auctions	p. 18
Revenue Equivalence	p. 20
Reserve Prices and Entry Fees	p. 22
The Correlated Private Values Model	p. 25
Second-price Auction	p. 26
First-price Auction	p. 27
Comparison of Expected Payment	p. 29
The Effect of Risk Aversion	p. 32
Revenue Comparison	p. 33
The Discrete Valuation Case	p. 34
Exercises	p. 35
Common Value	p. 39
An Example with Independent Signals	p. 40
First-price Auction	p. 40
Second-price Auction Example	p. 42
An Example with Correlated Types	p. 42
First-price Auction	p. 43
Second-price Auction	p. 45
The Symmetric Model with Two Bidders	p. 46
Second-price Auctions	p. 50
First-price Auctions	p. 51
Revenue Comparison	p. 54
Exercises	p. 55
Affiliated Values	p. 57
The General Model	p. 58
Second-price Auctions	p. 63
First-price Auctions	p. 65
English Auctions	p. 67
Expected Revenue Ranking	p. 68
The Effects of Risk Aversion	p. 70
Exercises	p. 73
Mechanism Design	p. 75
The Revelation Principle	p. 75
Direct Mechanisms	p. 79
Revenue Equivalence and the Optimal Auction	p. 83
Some Extensions	p. 89
Non-monotonic Marginal Valuation	p. 89
Correlated Values	p. 101
Several Objects	p. 115
Common Values Auction	p. 117
Exercises	p. 119
Multiple Objects	p. 121
Sequential Auctions	p. 122
Simultaneous Auctions	p. 124
Discriminatory Auctions	p. 125
Uniform price Auctions	p. 130
Optimal Auction	p. 137
Exercises	p. 143
Probability	p. 145
Probability Spaces	p. 145
Uncountable Sample Space Case	p. 147
Random Variables	p. 148
Random Vectors and their Distribution	p. 150
Independence of Random Variables	p. 152
The Distribution of the Maximum of Independent Random Variables	p. 152
The Distribution of the Second Highest Value	p. 153
Mean Value of Random Variables	p. 154
Conditional Probability	p. 156
Differential Equations	p. 159
The Simplest Differential Equation	p. 159
Integrating Factor	p. 159
Affiliation	p. 161
Convexity	p. 165
References	p. 169
Index of Notations	p. 173
Index of Proper Names	p. 175
Index	p. 177
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