Market Design: A Linear Programming Approach to Auctions and Matching

296 Pages·2018·3.674 MB·English

by  Martin Bichler

MarketDesign
ALinearProgrammingApproachtoAuctionsandMatching
The digital economy has led to many new services where supply is matched with
demand for various types of goods and services. More and more people and organi-
zations are now in a position to design market rules that are being implemented in
software.
The design of markets is challenging as it is necessary to consider the strategic
behaviorofmarketparticipants,psychologicalfactors,andcomputationalproblemsin
ordertoimplementtheobjectivesofadesigner.Marketmodelsineconomicshavenot
lost their importance, but recent years have led to many new insights and principles
for the design of markets which are beyond traditional economic theory. This book
introducesthefundamentalsofmarketdesign,anengineeringfieldconcernedwiththe
designofreal-worldmarkets.
MartinBichlerisProfessorofInformaticsattheTechnicalUniversityofMunich(TUM),
and a faculty member at the TUM School of Management. He is known for his aca-
demic work on market design, and he has acted as a consultant for private and public
organizations including regulators, telecoms, and procurement organizations. Projects
inwhichheisinvolvedincludethedesignofauctionsforindustrialprocurement,logis-
tics,advertising,fisheryaccessrights,andspectrumsales.Hisresearchaddressesalgo-
rithmic,game-theoretical,andbehavioralquestionsandhasappearedinleadingjournals
in computer science, economics, operations research, and management science. He is
currently Editor of Business and Information Systems Engineering and serves on the
editorialboardsofseveralacademicjournals.

Market Design
A Linear Programming Approach to
Auctions and Matching
MARTIN BICHLER
TechnicalUniversityofMunich
UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
OneLibertyPlaza,20thFloor,NewYork,NY10006,USA
477WilliamstownRoad,PortMelbourne,VIC3207,Australia
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79AnsonRoad,#06-04/06,Singapore079906
CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
education,learningandresearchatthehighestinternationallevelsofexcellence.
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107173187
DOI:10.1017/9781316779873
©MartinBichler2018
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2018
PrintedintheUnitedStatesofAmericabySheridanBooks,Inc.
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
ISBN978-1-107-17318-7Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy
ofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication,
anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,
accurateorappropriate.
TomywifeClaudiaandmydaughtersMonaandSonja

Contents
1 Introduction page1
1.1 MarketDesignandMechanismDesign 2
1.2 MarketDesignandMathematicalOptimization 3
1.3 OutlineoftheBook 4
1.3.1 PartI MicroeconomicFundamentals 5
1.3.2 PartII Multi-ObjectAuctionDesign 6
1.3.3 PartIII ApproximationandMatchingMarkets 7
1.3.4 PartIV Appendices:MathematicalOptimization 7
1.4 Acknowledgements 8
PartI MicroeconomicFundamentals
2 Game-TheoreticalBasics 11
2.1 Normal-FormGames 11
2.1.1 Dominant-StrategyEquilibrium 13
2.1.2 ParetoOptimality 13
2.1.3 NashEquilibrium 14
2.1.4 CorrelatedEquilibrium 17
2.1.5 FurtherSolutionConcepts 19
2.2 Extensive-FormGames 20
2.3 BayesianGames 22
2.3.1 BayesianNashEquilibrium 24
2.3.2 ExPostEquilibrium 25
2.4 GamesandHumanBehavior 26
2.5 Summary 27
2.6 ComprehensionQuestions 28
2.7 Problems 28
3 MechanismDesign 30
3.1 SocialChoice 31
3.1.1 VotingRules 31
3.1.2 Arrow’sImpossibility 33
viii Contents
3.2 UtilityFunctions 35
3.3 MechanismDesignTheory 39
3.4 Quasi-LinearMechanismDesign 42
3.4.1 Quasi-LinearUtilityFunctions 42
3.4.2 TheVickrey–Clarke–GrovesMechanism 44
3.4.3 TheMyerson–SatterthwaiteTheorem 46
3.5 Summary 48
3.5.1 RobustMechanismDesign 48
3.5.2 AlgorithmicMechanismDesign 49
3.5.3 DynamicMechanismDesign 49
3.5.4 Non-Quasi-LinearMechanismDesign 50
3.6 ComprehensionQuestions 51
3.7 Problems 51
4 Single-ObjectAuctions 53
4.1 Single-ObjectAuctionFormats 53
4.2 ModelAssumptions 54
4.3 EquilibriumBiddingStrategiesintheIPVModel 55
4.3.1 AscendingAuctions 56
4.3.2 Second-PriceSealed-BidAuctions 56
4.3.3 First-PriceSealed-BidAuctions 57
4.3.4 DescendingAuctions 60
4.4 ComparingEquilibriumOutcomes 60
4.5 RobustnessoftheRevenueEquivalenceTheorem 62
4.5.1 Risk-AverseBidders 62
4.5.2 InterdependentValues 64
4.5.3 AsymmetryofBidders 65
4.5.4 UncertaintyabouttheNumberofBidders 65
4.6 BidderCollusion 65
4.7 OptimalAuctionDesign 66
4.8 SelectedExperimentalResults 68
4.9 Summary 70
4.10 ComprehensionQuestions 71
4.11 Problems 71
PartII Multi-ObjectAuctionDesign
5 AnOverviewofMulti-ObjectAuctions 75
5.1 GeneralEquilibriumModels 75
5.2 Multi-UnitAuctionFormats 77
5.2.1 Sealed-BidMulti-UnitAuctionFormats 77
5.2.2 OpenMulti-UnitAuctionFormats 78
5.2.3 SequentialSales 80
Contents ix
5.3 Multi-ItemAuctionFormats 81
5.3.1 SimultaneousAuctions 81
5.3.2 CombinatorialAuctions 81
5.4 OnlineandDynamicAuctionDesign 83
5.5 Summary 83
5.6 ComprehensionQuestions 84
6 TheSimultaneousMulti-RoundAuctionFormat 85
6.1 SMRARules 85
6.2 TacticsintheSMRA 86
6.3 StrategicSituationsinSMRA 88
6.3.1 WarofAttrition 89
6.3.2 EnglishAuctionvs.WarofAttrition 93
6.4 Summary 95
6.5 ComprehensionQuestions 95
7 Sealed-BidMulti-ObjectAuctions 96
7.1 GenericBidLanguages 96
7.2 TheWinnerDeterminationProblem 98
7.3 PaymentRules 101
7.3.1 Pay-as-BidPaymentRules 101
7.3.2 Vickrey–Clarke–GrovesPaymentRules 101
7.3.3 Bidder-OptimalCorePaymentRules 105
7.4 EquilibriumBiddingStrategies 107
7.4.1 First-PriceSealed-BidAuctions 107
7.4.2 Bidder-OptimalCore-SelectingAuctions 111
7.5 Domain-SpecificCompactBidLanguages 111
7.5.1 ProcurementMarketswithEconomiesofScale
andScope 112
7.5.2 DistributedSchedulinginTVAdMarkets 117
7.6 CombinatorialDoubleAuctions 120
7.7 EmpiricalResults 121
7.8 Summary 122
7.9 ComprehensionQuestions 123
7.10 Problems 124
8 OpenMulti-ObjectAuctions 126
8.1 Primal–DualAuctionsforAssignmentMarkets 127
8.1.1 DualPricesandVCGPayments 128
8.1.2 AnAscendingAuctionfortheAssignmentProblem 131
8.2 GreedyAuctionsandMatroids 139