Theory of Conditional Games

251 Pages·2011·1.646 MB·English

by  Wynn C. Stirling

TheoryofConditionalGames
Gametheoryexplainshowtomakegoodchoiceswhendifferentdecisionmakershave
conflictinginterests.Theclassicalapproachassumesthatdecisionmakersarecommitted
tomakingthebestchoicesforthemselvesregardlessoftheeffectonothers,butsuch
an approach is less appropriate when cooperation, compromise, and negotiation are
important. This book describes conditional games, an extension of game theory that
accommodatesmultiplestakeholderdecision-makingscenarioswherecooperationand
negotiationaresignificantissuesandwherenotionsofconcordantgroupbehaviorare
important.Usingclassicalbinarypreferencerelationsasapointofdeparture,thebook
extendstheconceptofapreferenceorderingthatpermitsstakeholderstomodulatetheir
preferencesasfunctionsofthepreferencesofothers.Astheseconditionalpreferences
propagate through a group of decision makers, they create social bonds that lead to
notionsofgroupconcordance.
Thisbookisintendedforallstudentsandresearchersofdecisiontheoryandgame
theory,includingstudentsinartificialintelligence(especiallymultiagentsystemsand
distributedcontrol),economics,managementscience,psychology,analyticphilosophy,
andappliedmathematics.
wynnc.stirlingisaprofessorofElectricalandComputerEngineeringandDean
ofGraduateStudiesatBrighamYoungUniversity.Hiscurrentresearchinterestsinclude
multiagentdecisiontheory,estimationtheory,informationtheory,andstochasticpro-
cesses.Heistheauthororco-authorofmorethanseventypublications,includingthe
graduatetextMathematicalMethodsandAlgorithmsforSignalProcessing(withTodd
Moon)andthemonographSatisficingGamesandDecisionMaking.

THEORY OF CONDITIONAL
GAMES
WYNN C. STIRLING
BrighamYoungUniversity
cambridge university press
Cambridge,NewYork,Melbourne,Madrid,CapeTown,
Singapore,SãoPaulo,Delhi,Tokyo,MexicoCity
CambridgeUniversityPress
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107011748
©WynnC.Stirling2012
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2012
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationdata
Stirling,WynnC.
Theoryofconditionalgames/WynnC.Stirling.
p. cm.
Includesbibliographicalreferencesandindexes.
ISBN978-1-107-01174-8
1. Decisionmaking. 2. Gamesofstrategy(Mathematics) I. Title.
QA279.4.S762012
519.3–dc23 2011041577
ISBN978-1-107-01174-8Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofURLs
forexternalorthird-partyInternetWebsitesreferredtointhispublicationanddoesnot
guaranteethatanycontentonsuchWebsitesis,orwillremain,accurateorappropriate.
ToTony,Dave,andKate
Naturalscienceisanexpansionofobserving;technology,ofcontriving;
mathematics,ofunderstanding.
—MichaelPolanyi
PersonalKnowledge(UniversityofChicagoPress,1958)
Contents
Preface pageix
1 Sociality 1
1.1 Classicaltheory 6
1.2 Socialitymodels 8
1.3 Coordination 20
1.4 Uncertainty 23
1.5 Satisficing 24
1.6 Applications 24
1.7 Summary 30
2 Conditioning 32
2.1 Complexsocialmodels 34
2.2 Aggregation 44
2.3 Coherence 64
2.4 Utilitynetworks 66
2.5 Reframing 69
2.6 Summary 71
3 Solutions 73
3.1 ConditionedNashequilibria 74
3.2 Concurrentdecisions 75
3.3 Marginalization 75
3.4 Groupandindividualwelfare 76
3.5 Negotiation 78
3.6 Illustrativeexample 80
3.7 Sociation 85
3.8 Nondominance 88
vii
viii Contents
3.9 Conditionalsocialchoice 93
3.10 Summary 95
4 Coordination 96
4.1 Extrinsicversusintrinsiccoordination 96
4.2 Hardness 101
4.3 Hardnessforsingleagents 104
4.4 Mutualinformationandcoordination 111
4.5 Summary 124
5 Uncertainty 126
5.1 Unification 127
5.2 Summary 137
6 Satisficing 139
6.1 Erroravoidance 142
6.2 Failureavoidance 154
6.3 Satisficinggames 162
6.4 Satisficingcoherence 164
6.5 Satisficingcompromises 166
6.6 Satisficingsocialchoice 167
6.7 Coordination 169
6.8 Summary 172
7 Applications 174
7.1 Battleofthesexes 174
7.2 TheUltimatumgame 180
7.3 TheStagHuntgame 190
7.4 Thefamilywalk 197
7.5 Unmannedaerialvehiclecontrol 200
8 Conclusion 209
8.1 Learning 211
8.2 Modelidentification 213
8.3 Dynamicsystems 213
8.4 Finalthoughts 214
A Probability 216
A.1 Theusesofprobabilitytheory 216
A.2 Probabilitydistributiontheory 219
Bibliography 223
NameIndex 229
SubjectIndex 232
Preface
HypothesensindNetze,nurderwirdfangen,derauswirft.
Theoriesarenets:onlyhewhocastswillcatch.
—Novalis(FriedrichvonHardenberg)
DialogenundMonolog,1798
JohnDeweyobservedthat“Inscientificinquiry,thecriterionofwhatistaken
to be settled, or to be knowledge, is being so settled that it is available as
a resource in further inquiry; not being settled in such a way as not to be
subject to revision in further inquiry” [emphasis in original, Dewey, 1938,
pp. 8–9]. Game theory has been successfully applied to the subject matter
of general economic theory, particularly for competitive and market-driven
scenarioswhereindividualrationalitydominates.Itisfirmlyestablished;itis
settled.Infact,itissosettledthatitisavailableasaresourceforfurtherinquiry
intotheissueofmultistakeholderdecisionmakingforscenarioswheresocial
relationshipsextendbeyondself-interest.
The net cast by classical game theory, however, is designed to capture
the essential characteristics of multistakeholder decision scenarios where all
participants possess categorical (unconditional) preference orderings and are
committed to achieving the best individual outcomes for themselves. This
book revises game theory to cast a wider net designed to capture, in addi-
tion,decision-makingscenarioswherecooperation,compromise,negotiation,
and altruism are significant issues, and where notions of concordant group
behaviorareimportant.Usingclassicalbinarypreferencerelationsasapointof
departure,thebookextendstheconceptofapreferenceorderingtopermitstake-
holderstomodulatetheirpreferencesasfunctionsofthepreferencesofothers.
As these conditional preferences propagate through a group of autonomous
decision makers, they create social bonds that lead naturally to notions of
groupconcordance.Thisconceptisformalizedbydefiningaconditionalgame
ix