An Introduction to the Theory of Mechanism Design

263 Pages·2015·1.222 MB·English

by  Tilman Borgers, Daniel Krahmer, Roland Strausz

An Introduction
to the Theory
of Mechanism Design

An Introduction
to the Theory
of Mechanism Design
TilmanBörgers
Withachapterby
DanielKrähmerandRolandStrausz
3
3
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Börgers,Tilman.
Anintroductiontothetheoryofmechanismdesign/TilmanBörgers;withachapterby
DanielKrähmerandRolandStrausz.
p. cm.
Includesbibliographicalreferencesandindex.
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2014046427
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CONTENTS
Preface xi
Acknowledgments xv
1.Introduction 1
2.Screening 6
2.1.Introduction 6
2.2.PricingaSingleIndivisibleGood 6
2.3.NonlinearPricing 18
2.4.Bundling 27
2.5.RemarksontheLiterature 29
2.6.Problems 29
3.BayesianMechanismDesign:Examples 31
3.1.Introduction 31
3.2.SingleUnitAuctions 31
3.2.1.Setup 31
3.2.2.Mechanisms,DirectMechanisms,andtheRevelationPrinciple 33
3.2.3.CharacterizingIncentiveCompatibilityandIndividualRationality 36
3.2.4.ExpectedRevenueMaximization 39
3.2.5.WelfareMaximization 42
3.2.6.NumericalExamples 43
3.3.PublicGoods 45
3.3.1.Setup 45
3.3.2.Incentive-CompatibleandIndividuallyRationalDirectMechanisms 46
3.3.3.ExAnteandExPostBudgetBalance 47
3.3.4.WelfareMaximization 50
3.3.5.ProfitMaximization 57
3.3.6.ANumericalExample 58
3.4.BilateralTrade 63
3.4.1.Setup 63
3.4.2.DirectMechanisms 63
3.4.3.WelfareMaximization 65
vii
viii Contents
3.4.4.ProfitMaximization 72
3.4.5.ANumericalExample 73
3.5.RemarksontheLiterature 74
3.6.Problems 75
4.DominantStrategyMechanisms:Examples 76
4.1.Introduction 76
4.2.SingleUnitAuctions 78
4.2.1.Setup 78
4.2.2.Mechanisms,DirectMechanisms,andtheRevelationPrinciple 79
4.2.3.CharacterizingDominantStrategyIncentiveCompatibilityandExPost
IndividualRationality 80
4.2.4.CanonicalAuctions 81
4.3.PublicGoods 84
4.3.1.Setup 84
4.3.2.DirectMechanisms 85
4.3.3.CharacterizingDominantStrategyIncentiveCompatibilityandExPost
IndividualRationality 85
4.3.4.CanonicalMechanisms 87
4.3.5.ExPostExactBudgetBalance 88
4.4.BilateralTrade 90
4.4.1.Setup 90
4.4.2.DominantStrategyIncentive-CompatibleandExPostIndividually
RationalDirectMechanisms 90
4.4.3.CanonicalMechanisms 92
4.4.4.ExPostExactBudgetBalance 92
4.5.RemarksontheLiterature 93
4.6.Problems 93
5.IncentiveCompatibility 95
5.1.Introduction 95
5.2.Setup 95
5.3.WeakMonotonicity 96
5.4.CyclicalMonotonicity 99
5.5.CyclicalMonotonicityWhenOutcomesAreLotteries 102
5.6.One-DimensionalTypeSpaces 103
5.7.RichTypeSpaces 108
5.8.RevenueEquivalence 109
5.9.IndividualRationality 110
5.10.RemarksontheLiterature 111
5.11.Problems 111
ix Contents
6.BayesianMechanismDesign 113
6.1.Introduction 113
6.2.Setup 114
6.3.IndependentTypes 116
6.4.CorrelatedTypes 119
6.4.1.Framework 119
6.4.2.FailureofRevenueEquivalence 119
6.4.3.CharacterizingBayesianIncentiveCompatibility 120
6.4.4.ANumericalExample 124
6.4.5.IndividualRationalityandBudgetBalance 126
6.4.6.Discussion 127
6.5.RemarksontheLiterature 128
6.6.Problems 128
7.DominantStrategyMechanisms 130
7.1.Introduction 130
7.2.DominantStrategyIncentiveCompatibility 130
7.3.ImplementingEfficientDecisionRules 132
7.4.PositiveAssociationofDifferences 134
7.5.IndividualRationalityandBudgetBalance 137
7.6.RemarksontheLiterature 140
7.7.Problems 140
8.NontransferrableUtility 141
8.1.Introduction 141
8.2.TheGibbard–SatterthwaiteTheorem 142
8.2.1.Setup 142
8.2.2.StatementoftheResultandOutlineoftheProof 143
8.2.3.EveryMonotoneDirectMechanismIsDictatorial 146
8.3.DominantStrategyIncentiveCompatibilityonRestrictedDomains 149
8.4.BayesianIncentiveCompatibility 151
8.5.RemarksontheLiterature 152
8.6.Problems 153
9.InformationalInterdependence 155
9.1.Introduction 155
9.2.AnExample 156
9.3.ImpossibilityofImplementingWelfare-MaximizingDecisionRules 158
9.4.CharacterizingAllIncentive-CompatibleMechanisms 161
9.5.RemarksontheLiterature 163
9.6.Problems 163