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Contents

CHAPTER 1: Introduction

1.1 OUTLINE

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

CHAPTER 2: Arrow’s Theorem and Its Consequences

2.1 THE INTEGER PROGRAM

2.1.1 General Domains

2.2 SOCIAL CHOICE FUNCTIONS

2.2.1 Strategic Candidacy

2.3 MECHANISMS AND REVELATION

CHAPTER 3: Network Flow Problem

3.2 NETWORK FLOW PROBLEM

3.3 FLOW DECOMPOSITION

3.4 THE SHORTEST-PATH POLYHEDRON

3.4.1 Interpreting the Dual

3.4.2 Infinite Networks

CHAPTER 4: Incentive Compatibility

4.1 NOTATION

4.2 DOMINANT STRATEGY INCENTIVE COMPATIBILITY

4.2.1 2-Cycle Condition

4.2.2 Convex Type Spaces

4.2.3 Convex Valuations

4.3 REVENUE EQUIVALENCE

4.3.1 A Demand-Rationing Example

4.4 THE CLASSICAL APPROACH

4.5 INTERDEPENDENT VALUES

4.6 BAYESIAN INCENTIVE COMPATIBILITY

CHAPTER 5: Efficiency

5.1 VICKREY-CLARKE-GROVES MECHANISM

5.2 COMBINATORIAL AUCTIONS

5.4 ASCENDING AUCTIONS

5.4.1 Primal-Dual Algorithm

5.4.2 Incentives

5.4.3 Subgradient Algorithm

An Ascending Implementation of the Subgradient Algorithm

5.5 GROSS SUBSTITUTES

5.6 AN IMPOSSIBILITY

5.7 A RECIPE

CHAPTER 6: Revenue Maximization

6.1 WHAT IS A SOLUTION?

6.2 ONE-DIMENSIONAL TYPES

6.2.1 A Formulation

6.2.2 Optimal Mechanism for Sale of a Single Object

Dominant Strategy

6.2.3 Polyhedral Approach

Polymatroids

6.2.4 Ironing and Extreme Points

6.2.5 From Expected Allocations to the Allocation Rule

6.2.6 Correlated Types

6.2.7 The Classical Approach

From the Discrete to the Continuous

Interdependent Values

6.3 BUDGET CONSTRAINTS

6.3.1 The Continuous Type Case

6.4 ASYMMETRIC TYPES

6.4.1 Bargaining

6.5 MULTIDIMENSIONAL TYPES

6.5.1 Wilson’s Example

6.5.2 Capacity-Constrained Bidders

The BNIC Constraints

Simplification of Incentive Constraints

Optimal Auction Formulation and Solution

Monotonicity and the Conditional Virtual Values

CHAPTER 7: Rationalizability

7.1 THE QUASILINEAR CASE

7.2 THE GENERAL CASE

References

Index