Strategic Communication and Information Design Andrew Kosenko Submitted in partial fulfillment ...

204 Pages·2017·1.4 MB·English

EssaysinEconomicTheory: StrategicCommunicationandInformationDesign
AndrewKosenko
Submittedinpartialfulfillmentofthe
requirementsforthedegreeof
DoctorofPhilosophy
intheGraduateSchoolofArtsandSciences
COLUMBIAUNIVERSITY
2018
(cid:13)c 2018
AndrewKosenko
Allrightsreserved
ABSTRACT
EssaysinEconomicTheory: StrategicCommunicationandInformationDesign
AndrewKosenko
Thisdissertationconsistsoffouressaysineconomictheory. Allofthemfallun-
der the umbrella of economics of information; we study various models of game-
theoretic interaction between players who are communicating with others, and
have (or are able to produce) information of some sort. There is a large emphasis
ontheinterplayofinformation,incentivesandbeliefs.
In the first chapter we study a model of communication and persuasion be-
tween a sender who is privately informed and has state independent preferences,
andareceiverwhohaspreferencesthatdependontheunknownstate. Inamodel
with two states of the world, over the interesting range of parameters, the equi-
libria can be pooling or separating, but a particular novel refinement forces the
pooling to be on the most informative information structure in interesting cases.
We also study two extensions - a model with more information structures as well
asamodelwherethestateoftheworldisnon-dichotomous,andshowthatanalo-
gousresultsemerge.
In the second chapter, which is coauthored with Joseph E. Stiglitz and Jungy-
oll Yun, we study the Rothschild-Stiglitz model of competitive insurance markets
with endogenous information disclosure by both firms and consumers. We show
thatanequilibriumalwaysexists,(evenwithoutthesinglecrossingproperty),and
characterize the unique equilibrium allocation. With two types of consumers the
outcomeisparticularlysimple,consistingofapoolingallocationwhichmaximizes
the well-being of the low risk individual (along the zero profit pooling line) plus
a supplemental (undisclosed and nonexclusive) contract that brings the high risk
individual to full insurance (at his own odds). We also show that this outcome is
extremelyrobustandParetoefficient.
Inthethirdchapterwestudyagameofstrategicinformationdesignbetweena
sender, who chooses state-dependent information structures, a mediator who can
then garble the signals generated from these structures, and a receiver who takes
an action after observing the signal generated by the first two players. Among
the results is a novel (and complete, in a special case) characterization of the set
of posterior beliefs that are achievable given a fixed garbling. We characterize
a simple sufficient condition for the unique equilibrium to be uninformative, and
providecomparativestaticswithregardtothemediator’spreferences,thenumber
ofmediators,anddifferentinformationalarrangements.
In the fourth chapter we study a novel equilibrium refinement - belief-payoff
monotonicity. Weintroduceadefinition,arguethatitisreasonablesinceitcaptures
an attractive intuition, relate the refinement to others in the literature and study
someoftheproperties.
Contents
ListofFigures iii
Acknowledgements vi
Dedication ix
1 BayesianPersuasionwithPrivateInformation 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 RelationshiptoExistingLiterature . . . . . . . . . . . . . . . . . . . . 6
1.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 AGeneralModel: Non-dichotomousStates. . . . . . . . . . . . . . . . 43
1.5 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2 RevisitingRothschild-Stiglitz 62
2.1 TheModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.2 Rothschild-StiglitzwithSecretContracts . . . . . . . . . . . . . . . . . 69
2.3 ParetoEfficiencywithUndisclosedContracts . . . . . . . . . . . . . . 73
2.4 DefinitionofMarketEquilibrium . . . . . . . . . . . . . . . . . . . . . 77
2.5 EquilibriumAllocations . . . . . . . . . . . . . . . . . . . . . . . . . . 83
i
2.6 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.7 GeneralityoftheResult . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2.8 Extensions: Non-uniquenessofEquilibrium . . . . . . . . . . . . . . . 90
2.9 ExtensionstoCaseswithManyTypes . . . . . . . . . . . . . . . . . . 92
2.10 PreviousLiterature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
2.11 TheNo-disclosureLimitedInformationPriceEquilibria . . . . . . . . 97
2.12 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
2.13 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3 MediatedPersuasion: FirstSteps 115
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.2 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.3 BinaryModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.4 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
3.5 AuxiliaryResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
4 ThingsLeftUnsaid: TheBelief-PayoffMonotonicityRefinement 166
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.2 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
4.3 RelationshiptoOtherRefinements . . . . . . . . . . . . . . . . . . . . 174
4.4 ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Bibliography 185
ii
List of Figures
Π Π
1.1 Illustrationwithpoolingon ,andthedeviationto . . . . . . . . . . 29
L H
2.1 Breaking the RS separating equilibrium in the presence of undisclosed
contractsathigh-riskodds. . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.2 Sustaininganequilibriuminthepresenceofacream-skimmingdeviant
contractDin z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.3 Pareto-efficientallocations((A∗,C∗),(A(cid:48),C(cid:48)))andtheequilibriumallo-
cation (A∗,C∗). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.4 Equilibriumwithoutsingle-crossing. . . . . . . . . . . . . . . . . . . . . . 91
2.5 Equilibrium (A,B,C) with three types, which cannot be broken by D
as individuals of higher-risk type supplement it by additional pooling
insurance(alongthearrow)withoutbeingdisclosedtothedeviantfirm.
P denotestheaverageprobabilityofaccidentforthetwohighestrisk
−L
types,whileV indicatesanindifferencecurvefori-risktype(i = H,M,L). 93
i
2.6 Breaking No-Disclosure-Information Price Equilibrium Pe by a fixed-
quantitycontract (α(cid:48),β(cid:48)),where Pe > P(cid:48) > P. . . . . . . . . . . . . . . . . 101
iii
2.7 Nash Equilibrium can be sustained against multiple deviant contracts
(A∗B,G) or (A∗B(cid:48),G) offered at different prices as high-risk individu-
alsalsochooseG(over A∗B)oras(A∗B(cid:48),G)yieldslossesforthedeviant
firm(whileinducingself-selection). . . . . . . . . . . . . . . . . . . . . . . 112
3.1 IllustrationoftheModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
3.2 EffectofGarblingonBeliefsinaDichotomy. . . . . . . . . . . . . . . . . 125
3.3 AnExample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.4 ComparingtheFeasibleSetsofPosteriors. . . . . . . . . . . . . . . . . . . 141
3.5 IncreasingNoiseShrinkstheSetofFeasiblePosteriors. . . . . . . . . . . 142
3.6 TracingtheOuterLimitof F(M,π): FirstBoundary. . . . . . . . . . . . . 144
3.7 TracingtheOuterLimitof F(M,π): SecondBoundary. . . . . . . . . . . . 145
3.8 TracingtheOuterLimitof F(M,π): ThirdBoundary. . . . . . . . . . . . 146
3.9 TracingtheOuterLimitof F(M,π): FourthBoundary. . . . . . . . . . . . 147
3.10 F(M,π): anIllustration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.11 KeyFeaturesoftheFeasibleSet. . . . . . . . . . . . . . . . . . . . . . . . . 149
3.12 Blackwell’sOrderImpliesSetInclusionforFeasibleSets. . . . . . . . . . 153
3.13 FurtherIllustrationofSetInclusion. . . . . . . . . . . . . . . . . . . . . . 154
3.14 UnrankedFeasibleSets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
3.15 GoingBeyondtheDichotomy: ThreeSignals. . . . . . . . . . . . . . . . 156
3.16 ASimpleNon-trivialExample. . . . . . . . . . . . . . . . . . . . . . . . . 157
4.1 ICandBPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
4.2 D1andBPMmakethesameselection. . . . . . . . . . . . . . . . . . . . . 177
iv
4.3 NWBRandBPMmakethesameselection. . . . . . . . . . . . . . . . . . . 178
4.4 D1andBPMmakedifferentselections. . . . . . . . . . . . . . . . . . . . . 178
4.5 D1vs. BPM:whichismoreconvincing? . . . . . . . . . . . . . . . . . . . 180
4.6 D1doesnotapply,BPMdoes. . . . . . . . . . . . . . . . . . . . . . . . . . 180
4.7 Abestiaryofrefinementconcepts. . . . . . . . . . . . . . . . . . . . . . . 181
v
Acknowledgements
It is with a profound sense of gratitude and humility that I write these words. I
feelthatmydebttothepeoplewhomadethejourneypossibleisgreaterthanthat
ofmostotherstudents.
There is one person I want to thank before and above all others - my advisor,
Navin Kartik. He has been an exceptional role model even before becoming my
advisor (in fact, before I even started the program), and will always remain so. It
is indeed rare that such a razor-sharp wit should be combined with deep under-
standing, and wide knowledge with a warm personality and wisdom. He pushed
metobecomemybest,supportedmeinsomanyways,farbeyondanyobligation,
andbelievedinmeevenwhenIdidn’tbelieveinmyself.
IwouldalsoliketothankandnotemyprofounddebttoJosephStiglitz. Work-
ingwithJoehasbeenaonce-in-a-lifetimeprivilege. Hehasbeenincrediblygener-
ous with his time, a great mentor and a true joy to work with. He has also effec-
tively functioned as an unofficial advisor and I will forever cherish the experience
of discussing economic ideas with him as the sun set on the Hudson River. Joe
hasalwaysbeenawellspringofideascombinedwithaprofoundethicalcompass,
withunparalleledpublicspiritandanexemplaryworkethic.
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