book

Auction Theory, 2nd Edition

Name: Auction Theory, 2nd Edition
Author: Vijay Krishna
ISBN: 9780080922935

by Vijay Krishna

September 2009

Intermediate to advanced

336 pages

9h 37m

English

Academic Press

Read now

Unlock full access

Front Cover
Title Page
Copyright Page
Dedication Page
Table of Contents
Preface
Chapter 1. Introduction
1.1 Some Common Auction Forms
1.2 Valuations
1.3 Equivalent Auctions
1.4 Revenue versus Efficiency

1.5 What Is an Auction?
1.6 Outline of Part I
Part I: Single-Object Auctions
Chapter 2. Private Value Auctions: A First Look
2.1 The Symmetric Model
2.2 Second-Price Auctions
2.3 First-Price Auctions
2.4 Revenue Comparison
2.5 Reserve Prices (1/2)
2.5 Reserve Prices (2/2)
Chapter 3. The Revenue Equivalence Principle
3.1 Main Result
3.2 Some Applications of the Revenue Equivalence Principle (1/2)
3.2.1 Unusual Auctions3.2.2 Uncertain Number of Bidders
3.2 Some Applications of the Revenue Equivalence Principle (2/2)
Chapter 4. Qualifications and Extensions
4.1 Risk-Averse Bidders
4.2 Budget Constraints
4.2.1 Second-Price Auctions4.2.2 First-Price Auctions4.2.3 Revenue Comparison
4.3 Asymmetries among Bidders (1/2)
4.3.1 Asymmetric First-Price Auctions with Two Bidders
4.3 Asymmetries among Bidders (2/2)
4.3.2 Revenue Comparison4.3.3 Efficiency Comparison
4.4 Resale and Efficiency (1/2)
4.4 Resale and Efficiency (2/2)
Chapter 5. Mechanism Design
5.1 Mechanisms5.1.1 The Revelation Principle5.1.2 Incentive Compatibility
5.1.3 Individual Rationality
5.2 Optimal Mechanisms (1/2)
5.2.1 Setup5.2.2 Solution5.2.3 Discussion and Interpretation
5.2 Optimal Mechanisms (2/2)
5.2.4 Auctions versus Mechanisms
5.3 Efficient Mechanisms (1/2)
5.3.1 The VCG Mechanism5.3.2 Budget Balance5.3.3 An Application to Bilateral Trade
5.3 Efficient Mechanisms (2/2)
Chapter 6. Auctions with Interdependent Values
6.1 The Symmetric Model
6.2 Second-Price Auctions
6.3 English Auctions
6.4 First-Price Auctions
6.5 Revenue Comparisons
6.5.1 English versus Second-Price Auctions6.5.2 Second-Price versus First-Price Auctions
6.6 Efficiency
Chapter 7. The Revenue Ranking (“Linkage”) Principle
7.1 The Main Result
7.2 Public Information
7.3 An Alternative Linkage Principle
Chapter 8. Asymmetries and Other Complications
8.1 Failures of the Linkage Principle
8.2 Asymmetric Equilibria in Symmetric Second-Price Auctions
8.3 Asymmetrically Informed Bidders
8.4 Reserve Prices and Entry Fees (1/2)
8.4 Reserve Prices and Entry Fees (2/2)
Chapter 9. Efficiency and the English Auction
9.1 The Single Crossing Condition
9.2 Two-Bidder Auctions
9.3 The Average Crossing Condition
9.4 Three or More Bidders
9.5 Proof of Proposition 9.2
9.6 Miscellany
Chapter 10. Mechanism Design with Interdependent Values
10.1 Efficient Mechanisms
10.2 Optimal Mechanisms (1/2)
10.2 Optimal Mechanisms (2/2)
Chapter 11. Bidding Rings
11.1 Collusion in Second-Price Auctions (1/2)
11.1.1 Efficient Collusion
11.1 Collusion in Second-Price Auctions (2/2)
11.1.2 Reserve Prices in the Face of Collusion
11.2 Collusion in First-Price Auctions
Part II: Multiple-Object Auctions
Chapter 12. An Introduction to Multiple-Object Auctions
12.1 Sealed-Bid Auctions for Selling Identical Units
12.1.1 Discriminatory Auctions12.1.2 Uniform-Price Auctions12.1.3 Vickrey Auctions
12.2 Some Open Auctions (1/2)
12.2.1 Dutch Auctions12.2.2 English Auctions12.2.3 Ausubel Auctions
12.2 Some Open Auctions (2/2)
Chapter 13. Equilibrium and Efficiency with Private Values
13.1 The Basic Model
13.2 Vickrey Auctions
13.3 Efficiency in Multiunit Auctions
13.4 Uniform-Price Auctions (1/2)
13.4.1 Demand Reduction
13.4 Uniform-Price Auctions (2/2)
13.4.2 Single-Unit Demand
13.5 Discriminatory Auctions (1/2)13.5.1 Structure of Equilibria13.5.2 Single-Unit Demand
13.5 Discriminatory Auctions (2/2)
Chapter 14. Some Revenue Considerations
14.1 Revenue Equivalence in Multiunit Auctions
14.2 Revenue Equivalence with Multiunit Demand: An Example (1/2)
14.2 Revenue Equivalence with Multiunit Demand: An Example (2/2)
Chapter 15. Sequential Sales
15.1 Sequential First-Price Auctions15.1.1 Two Units15.1.2 More than Two Units
15.1.3 Equilibrium Bids and Prices
15.2 Sequential Second-Price Auctions (1/2)
15.2.1 Revenue Equivalence15.2.2 Equilibrium Bids
15.2 Sequential Second-Price Auctions (2/2)
Chapter 16. Nonidentical Objects
16.1 The Model
16.2 Efficient Allocations
16.3 Substitutes and Complements
16.4 Bundling
16.5 Some Computational Issues
16.6 Budget Constraints
Chapter 17. Packages and Positions
17.1 Package Auctions
17.1.1 The Ascending Auction17.1.2 Gross Substitutes17.1.3 Equilibrium of the Proxy Auction
17.2 Position Auctions (1/2)
17.2 Position Auctions (2/2)
Chapter 18. Multiple Objects and Interdependent Values
18.1 One-Dimensional Signals18.1.1 An Efficient Direct Mechanism18.1.2 Efficiency via Open Auctions
18.2 Multidimensional Signals (1/2)
18.2.1 Single Object18.2.2 Multiple Objects
18.2 Multidimensional Signals (2/2)
Part III: Appendices
Appendix A. Continuous Distributions (1/2)
Appendix A. Continuous Distributions (2/2)
Appendix B. Stochastic Orders (1/2)
Appendix B. Stochastic Orders (2/2)
Appendix C. Order Statistics
Appendix D. Affiliated Random Variables
Appendix E. Some Linear Algebra (1/2)
Appendix E. Some Linear Algebra (2/2)
Appendix F: Games of Incomplete Information
Appendix G. Existence of Equilibrium in First-Price Auctions (1/2)
Appendix G. Existence of Equilibrium in First-Price Auctions (2/2)
Bibliography (1/2)
Bibliography (2/2)
Index (1/2)
Index (2/2)

Content preview from Auction Theory, 2nd Edition

5.2 Optimal Mechanisms 67

5.2 OPTIMAL MECHANISMS

In this section we view the seller as the designer of the mechanism and examine

mechanisms that maximize the expected revenue—the sum of the expected

payments of the buyers—among all mechanisms that are incentive compatible

and individually rational. We reiterate that when carrying out this exercise, the

revelation principle guarantees that there is no loss of generality in restricting

attention to direct mechanisms.

We will refer to a mechanism that maximizes expected revenue, subject to

the incentive compatibility and individual rationality constraints, as an optimal

mechanism.

5.2.1 Setup

Suppose that ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.

Read now

Unlock full access

More than 5,000 organizations count on O’Reilly

O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.

Julian F.

Head of Cybersecurity

I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.

Addison B.

Field Engineer

I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.

Amir M.

Data Platform Tech Lead

I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.

Mark W.

Embedded Software Engineer

The Human Factor in AI-Based Decision-Making

Publisher Resources

ISBN: 9780123745071

Cloud Computing

Data Engineering

Data Science

AI & ML

Programming Languages

Software Architecture

IT/Ops

Security

Design

Business

Soft Skills

Auction Theory, 2nd Edition

by Vijay Krishna

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.