theory of mechanism design
TRANSCRIPT
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An Introduction to the Theory
of Mechanism Design
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Acknowledgments
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Contents
Acknowledgments ii
Preface ix
1 Introduction 1
2 Screening 6
3 Bayesian Mechanism Design: Examples 33
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4 Dominant Strategy Mechanisms: Examples 82
5 Incentive Compatibility 103
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6 Bayesian Mechanism Design 122
7 Dominant Strategy Mechanisms 141
8 Non-Transferrable Utility 153
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9 Informational Interdependence 169
10 Robust Mechanism Design 180
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11 Dynamic Mechanism Design 226
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http:
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Chapter 1
Introduction
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Chapter 2
Screening
2.1 Introduction
2.2 Pricing a Single Indivisible Good
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Proposition 2.1 .
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Definition 2.2.
Definition 2.3.
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Lemma 2.1.
Lemma 2.2.
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Lemma 2.3 .
Lemma 2.4 .
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Proposition 2.2.
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Lemma 2.6.
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Definition 2.4.
Proposition 2.4.
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Lemma 2.7.
Proposition 2.5.
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2.3 Nonlinear Pricing
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Definition 2.5.
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Assumption 2.1.
Proposition 2.6.
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Example 2.1.
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2.4 Bundling
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Chapter 3
Bayesian Mechanism Design:
Examples
3.1 Introduction
3.2 Single Unit Auctions
3.2.1 Set-Up
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3.2.2 Mechanisms, Direct Mechanisms, and the Revelation
Principle
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Definition 3.1.
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Proposition 3.1 .
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Definition 3.2.
Definition 3.3.
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3.2.3 Characterizing Incentive Compatibility and Individual
Rationality
Lemma 3.1.
Lemma 3.2.
Lemma 3.3 .
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Lemma 3.4 .
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Proposition 3.2.
Proposition 3.3.
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3.2.4 Expected Revenue Maximization
Lemma 3.5.
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Assumption 3.1.
Proposition 3.4 .
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3.2.5 Welfare Maximization
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Proposition 3.5.
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3.2.6 Numerical Examples
Example 3.1.
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3.3.2 Incentive-Compatible and Individually Rational Direct
Mechanisms
Definition 3.4.
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3.3.3 Ex ante and Ex post Budget Balance
Definition 3.5.
Definition 3.6.
Definition 3.7.
Proposition 3.6.
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Proposition 3.7.
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Definition 3.8.
Lemma 3.6.
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Lemma 3.8.
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Assumption 3.2.
Proposition 3.8.
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3.3.5 Profit Maximization
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Proposition 3.9.
3.3.6 A Numerical Example
Example 3.3.
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Proposition 3.10.
Proposition 3.11.
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3.4.2 Direct Mechanisms
Definition 3.9.
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3.4.3 Welfare Maximization
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Proposition 3.12 .
Definition 3.10.
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Lemma 3.9.
Lemma 3.10.
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Lemma 3.11.
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Assumption 3.3.
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Proposition 3.13.
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3.4.4 Profit Maximization
Proposition 3.14.
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3.4.5 A Numerical Example
Example 3.4.
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Proposition 3.15.
Proposition 3.16.
3.5 Remarks on the Literature
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3.6 Problems
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Chapter 4
Dominant Strategy
Mechanisms: Examples
4.1 Introduction
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4.2 Single Unit Auctions
4.2.1 Set-Up
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4.2.2 Mechanisms, Direct Mechanisms, and the Revelation
Principle
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Proposition 4.1 .
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Definition 4.1.
Definition 4.2.
4.2.3 Characterizing Dominant Strategy Incentive Compat-
ibility and Ex Post Individual Rationality
Proposition 4.2.
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Proposition 4.3.
4.2.4 Canonical Auctions
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Definition 4.3.
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Proposition 4.4.
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4.3.2 Direct Mechanisms
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Proposition 4.6.
4.3.4 Canonical Mechanisms
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Definition 4.4.
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Proposition 4.7.
4.3.5 Ex Post Exact Budget Balance
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Proposition 4.8.
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4.4 Bilateral Trade
4.4.1 Set-Up
4.4.2 Dominant Strategy Incentive Compatible and Ex Post
Individually Rational Direct Mechanisms
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4.4.3 Canonical Mechanisms
Definition 4.5.
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Proposition 4.11.
4.4.4 Ex Post Exact Budget Balance
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Proposition 4.12.
4.5 Remarks on the Literature
4.6 Problems
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Chapter 5
Incentive Compatibility
5.1 Introduction
5.2 Set-Up
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Definition 5.1.
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Definition 5.2.
5.3 Weak Monotonicity
Definition 5.3.
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Definition 5.4.
Proposition 5.1.
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5.4 Cyclical Monotonicity
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Definition 5.5.
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Proposition 5.2.
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5.5 Cyclical Monotonicity When Outcomes Are
Lotteries
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Proposition 5.3.
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5.6 One-Dimensional Type Spaces
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Definition 5.6.
Definition 5.7.
Proposition 5.4.
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Definition 5.8.
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Proposition 5.5.
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Definition 5.9.
Proposition 5.6.
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5.7 Rich Type Spaces
Definition 5.10.
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Proposition 5.7.
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5.8 Revenue Equivalence
Proposition 5.8.
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5.9 Individual Rationality
Definition 5.11.
Proposition 5.9.
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5.10 Remarks on the Literature
5.11 Problems
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Chapter 6
Bayesian Mechanism Design
6.1 Introduction
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6.2 Set-Up
Definition 6.1.
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6.3 Independent Types
Proposition 6.1.
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Proposition 6.2.
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Proposition 6.3.
6.4 Correlated Types
6.4.1 Framework
6.4.2 Failure of Revenue Equivalence
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6.4.4 A Numerical Example
Example 6.1.
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6.4.5 Individual Rationality and Budget Balance
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Definition 6.8.
Proposition 6.6.
6.4.6 Discussion
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6.5 Remarks on the Literature
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6.6 Problems
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Chapter 7
Dominant Strategy
Mechanisms
7.1 Introduction
7.2 Dominant Strategy Incentive Compatibility
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Definition 7.1.
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Definition 7.2.
Proposition 7.1.
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Proposition 7.2.
Proposition 7.3.
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7.3 Implementing Efficient Decision Rules
Definition 7.3.
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Definition 7.4.
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Proposition 7.4.
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Corollary 7.1.
7.4 Positive Association of Differences
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Definition 7.5.
Proposition 7.5.
Definition 7.6.
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Proposition 7.8.
7.5 Individual Rationality and Budget Balance
Definition 7.7.
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Proposition 7.9.
Definition 7.8.
Proposition 7.10.
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7.6 Remarks on the Literature
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7.7 Problems
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Chapter 8
Non-Transferrable Utility
8.1 Introduction
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8.2 The Gibbard Satterthwaite Theorem
8.2.1 Set Up
Definition 8.1.
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Definition 8.2.
8.2.2 Statement of the Result and Outline of the Proof
Definition 8.3.
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Proposition 8.1.
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Definition 8.4.
Proposition 8.2.
Definition 8.5.
Proposition 8.3.
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Definition 8.6.
Proposition 8.4.
8.2.3 Every monotone direct mechanism is dictatorial
Proposition 8.5.
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Proposition 8.6.
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8.4 Bayesian Incentive Compatibility
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8.5 Remarks on the Literature
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8.6 Problems
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Chapter 9
Informational
Interdependence
9.1 Introduction
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9.2 An Example
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9.4 Characterizing All Incentive Compatible
Mechanisms
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9.5 Remarks on the Literature
9.6 Problems
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Chapter 10
Robust Mechanism Design
10.1 Introduction
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10.2 An Example
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10.3 Modeling Incomplete Information
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10.3.1 Hierarchies of Beliefs
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Definition 10.1.
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10.3.2 Type spaces
Definition 10.2.
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10.3.3 Common Prior Type Spaces
Definition 10.4.
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Proposition 10.1.
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10.4 The Mechanism Designers Uncertainty
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Definition 10.5.
Definition 10.6.
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Definition 10.7.
10.5 Mechanisms
Definition 10.8.
Definition 10.9.
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Definition 10.10.
10.6 Bayesian Equilibria and the Revelation Prin-
ciple
Definition 10.11.
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Proposition 10.2.
Definition 10.12.
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Proposition 10.4.
Proposition 10.5.
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10.7.1 Belief Revelation
Proposition 10.6.
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10.7.2 Betting
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Proposition 10.7.
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10.7.3 Equilibrium Outcomes and Payoff Types
Proposition 10.8.
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Proposition 10.9.
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10.8 Robust Mechanism Design With a Common
Prior
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10.9 Robust Mechanism Design Without a Com-
mon Prior
10.9.1 The Mechanism Designers Objectives
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Definition 10.14.
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Definition 10.15.
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10.9.2 Undominated Mechanisms
Definition 10.16.
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10.10 Conceptual Problems in the Quasi-Linear
Case
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Proposition 10.10.
Proposition 10.11.
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10.11 Voting Revisited
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Definition 10.17.
Definition 10.18.
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Proposition 10.12.
Definition 10.19.
Definition 10.20.
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Proposition 10.13.
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Proposition 10.14.
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Definition 10.21.
Proposition 10.15.
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10.12 Remarks on the Literature
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10.13 Problems
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Chapter 11
Dynamic Mechanism Design
by Daniel Krahmer and Roland Strausz
11.1 Introduction
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11.2 Dynamic Private Information
11.2.1 Sequential Screening
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Definition 11.1.
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Proposition 11.1.
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Definition 11.2.
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Definition 11.3.
Proposition 11.2.
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Proposition 11.3.
Proposition 11.4.
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Proposition 11.5.
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Proposition 11.6.
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Proposition 11.7.
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Assumption 11.1.
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11.2.2 The role of private information
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Proposition 11.10.
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11.2.3 Sequential Mechanism Design
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Assumption 11.2.
Proposition 11.11.
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Definition 11.4.
R
Definition 11.5.
Definition 11.6.
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Proposition 11.12.
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11.4 Remarks on the Literature
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11.5 Problems
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R
R
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R
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http:
//faculty.haas.berkeley.edu/hermalin/
http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/http://faculty.haas.berkeley.edu/hermalin/ -
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Index
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