rabin's theorem...grading: the grades given: a-f, with a as the best and e as the weakest...
TRANSCRIPT
ECON42601BehavioralEconomics Candidate172504
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CandidateinstructionsECON4260–BehavioralEconomicsThisissomeimportantinformationaboutthewrittenexaminECON4260.Pleasereadthiscarefullybeforeyoustartansweringtheexam.Dateofexam:Friday,December14,2018Timeforexam:14.30–17.30Theproblemset:Theproblemsetconsistsoffourquestions,withseveralsub-questions.Theycountasindicated.Startbyreadingthroughthewholeexam,andmakesurethatyouallocatetimetoansweringproblemsyoufindeasy.Youcangetagoodgradeeveniftherearepartsofproblemsthatyoudonothavetimetosolve.Multiplechoicequestionsaregradedsuchthatyouwillalwaysbebetteroffprovidingananswer,thantoleaveitblank.Sketches:Inthisexam,youmayusesketchesonquestions1b,1d,1e,andquestions3and4withsub-questions.Youaretousethesketchingsheetshandedtoyou.Youcanusemorethanonesketchingsheetperquestion.Seeinstructionsforfillingoutsketchingsheetsonyourdesk.Itisveryimportantthatyoumakesuretoallocatetimetofillintheheadings(thecodeforeachproblem,candidatenumber,coursecode,dateetc.)onthesheetsthatyouwillusetoaddtoyouranswer.Youwillfindthecodeforeachproblemundertheproblemtext.YouwillNOTbegivenextratimetofilloutthe"generalinformation"onthesketchingsheets(taskcodes,candidatenumberetc.)DoNOThandinsketchesonotherquestionsthanquestions1b,1d,1eandquestions3and4.Sketcheshandedinforotherquestions,willnotbeincludedintheassessment.
Resourcesallowed:Nowrittenorprintedresources-orcalculator-isallowed(exceptifyouhavebeengranteduseofadictionaryfromtheFacultyofSocialSciences).
Grading:Thegradesgiven:A-F,withAasthebestandEastheweakestpassinggrade.Fisfail.Gradesaregiven:Tuesday8January2019.
1 0 7 7 7 1 8
1(a) Rabin'sTheorem
Attachingsketchestothisquestion?Usethefollowingcode:
(3points)
Inthisquestionyouarenotsupposedtohandinsketches.
Assumethatapersonwhomaximizesexpectedutilityisindifferentbetweengetting0kronerwithcertaintyandalotterythatgives+100kronerwith60%probabilityand-100kronerwiththeremainingprobability.Wenormalizetheutilitysuchthat and ,where ishiscurrentwealth.
Compute 5
Correct.3of3marks.
1(b) Rabin'sTheorem(continued)(7points)
Inthisquestionyoucanhandinsketches.Usethesketchingpaperhandedtoyouintheexaminationvenue.Seeinstructionsonyourdesk.
RabinandThaler(2001),inthecoursereadinglist,extendthiskindofcalculation.IntheexamplediscussedinProblem1a,ispossibletoshowthat ,foranyvalueof .(Youarenotaskedtoshowthis.)
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8 1 8 8 7 2 3Attachingsketchestothisquestion?Usethefollowingcode:
Whatextraassumptionsareneededtoreachthiskindofconclusion?
Fillinyouranswerhereand/oronsketches
Atpersonenmaksimererexpectedutility,ogatpersonenavslårveddemåletuansetthvormyepengerhanhar("irrespectiveofwealth")
Answered.
7 8 0 0 1 1 9
1(c) Rabin'sTheorem(continued)
Attachingsketchestothisquestion?Usethefollowingcode:
(2pointspercorrectanswer)
Inthisquestionyouarenotsupposedtohandinsketches.
ConsideralotterywherethepersoninProblem1a-bcanwinanamount withprobabilityp,where isequaltothevaluetheNorweganOilfund.Withtheremainingprobabilitythepersonloses100kroner.
Ifitwasthecasethat ,whatwouldbetheexpectedutilityofthislotteryinthefollowingtwocases?
p=20% 1.8
p=40% 3.6
WouldthepersoninProblem1a-b,acceptthelotterywithp=40%? Yes (Yes,No)
Correct.6of6marks.
1(d) Rabin'sTheorem(continued)(9points)
Inthisquestionyoucanhandinsketches.Usethesketchingpaperhandedtoyouintheexaminationvenue.Seeinstructionsonyourdesk.
Intheirpaper(inthecoursereadinglist),RabinandThalerstatethat:“weaspiretohavewrittenoneofthelastarticlesdebatingthedescriptivevalidityoftheexpectedutilityhypothesis.”Theirpaperisbasedoncalculationslikethoseintheproblemsabove.
Explainwhytheresultsintheproblemsaboveandsimilarcalculationsareconsideredaproblemforexpectedutilitytheory,butnotforprospecttheory.
Fillinyouranswerhereand/oronsketches
Detatenexpectedutilitymaximizervisersegåtakkeneitilsmåbetsmedpositivforventningsverdi,forutsetteratdeharenheltekstremlossaversion.Idettetilfelleterdetjosnakkomatdetakkerneitilen20%sjanseforåtjenetilsvarendemengdepengersomoljefondetdersomdeteren80%foratdetaper100kroner.Såforatexpectedutilityskalgimening,børmanværetilnærmetrisikonøytraltilsmåbetsmedpositivforventningsverdialadetviharsettpåtilnå.Menlikevelviserdetsegaltsåatmangetakkerneitilsånnebets.Noenmåterprospecttheoryskillersegfraexpectedutilityergjennom:
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6 5 2 7 2 0 2Attachingsketchestothisquestion?Usethefollowingcode:
-lossaversion-referencepoint-diminishingsensitivity-decisionweightLossaversioninnebærerattapoggevinstavsammesumopplevesveldigforskjelligavdemedprospecttheory-preferanser.Tapetvilsvimyemerenngevinstengjør.Dettehengersammenmedbrukenavenvaluefunction,somforeksempelkanseslikut:xhvisx_>0v(x)=2.5xhvisx<0Detbetyratetbetmed50%sannsynlighetforåvinne200,og50%sannsynlighetforåtape100,vilavenmedPT-preferanserevalueresslik:0,5*200+0,5*2,5*(-100)=100-125=-25EnmedEU-preferanservilimidlertidevalueredetsom(gittatvinormalisereru(0)=0):0,5*200+0,5*(-100)=100-50=50SåsammebetvilaltsåværeulønnsomtforenmedPT-preferanser,menlønnsomtforenmedEU-preferanser.SådefunnaRabinhargjortpasserikkemedteorienomatvimaksimererexpectedutility.Fordavilleviikkesagtnettiletsånntypebet.Rabinskriverideneneartikkelenathanønskeratvimåkutteutexpectedutility,oghellerforklarevalgenemenneskergjørmedenkombinasjonavlossaversionogtendensenmenneskerhartilåvurdererisikoersomenkelttilfelleristedetforstørregrupperavrisikoer.Lossaversionforklartejegnettopp.Detandrehandleromatdetiexpectedutilityberegnesdessutenverdienavbetsutfraabsolutteforandringeriwealth,mensdetiprospecttheoryvurderesutfraetreferansepunktmansetter.Såforeksempelvileksempeletjeggaovermed50%sannsynlighetforåvinne200,og50%sannsynlighetforåtape100kunnevurderesannerledesavenmedPT-preferanserdersommanutførerveddemålettoganger-doglittavhengigavhvordandevelgerreferansepunktet.Dersommanevaluererognullstilleretterførstegjennomføringavveddemålet,vilingentingforandres.Davilreferansepunktetpåenmåteværetilbaketilnull.ogmangjennomførerveddemåletpånyttmeddetsomutgangspunkt,noevivisteoveratvilleværeulønnsomt,medforvnetetverdi-25(gittvaluefunctionjegvalgte).Dersommanimidlertidserpåveddemål1somendelavenstørreportfolioavveddemål,vildetimidlertidfåpositivforventningsverdiåsija:Sannsynlighetenforåtape200kroner:0,5*0,5=0,25Sannsynlighetenforåvinne400kroner:0,5*0,5=0,25Sannsynlighetenforåvinne100kroner:0,5Altåsblirforventetverdi:v=0,25*400+0,5*100+0,25*2,5*(-200)=100+50-125=25.
Answered.
1(e) Rabin'sTheorem(continued)
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1 7 4 5 6 1 6Attachingsketchestothisquestion?Usethefollowingcode:
(5points)
Inthisquestionyoucanhandinsketches.Usethesketchingpaperhandedtoyouintheexaminationvenue.Seeinstructionsonyourdesk.
Expectedutilitytheoryisstillmuchusedineconomictheory,alsoinappliedanalyses.
Whydoyouthinkexpectedutilitytheoryisstillsomuchused?(Therearenocorrectanswershere.Youranswerswillbegradedbasedoncoherenceandrelevanceofyourarguments.)
Fillinyouranswerhereand/oronsketches
Kandetkanskjeskyldesatadferdsøkonomitildelsfortsatteren"ny"grenavøkonomien,ogatdeterentidkrevendeprosessåfåetablertnyemodeller,spesieltnårdetgårpåbekostningavmodellerogmetodermanharbruktgjennomalletider.Expectedutilityernokdessutenenganskeintuitivtilnærmingtilslikeproblemer,ogentilnærmingsomerveldiglettåforståsegpåogandvendeselv.Kanskjekandetogsåskyldesatdetikkenødvendigvisharblittetablertnoenandresærliggodealternativer.Forinntrykketmittfraåhalestpensum,eratendelforskeremeneratogsåprospecttheoryharsinesvakheter,ogernoeutdatert.Såkanskjeventermanpåatnoenskalkommemedenlittmeroppdatertmodellforåstudereslikeprobleme.
Answered.
2 Decisionmakerswithself-controlproblems(3pointspercorrectanswer)Inthisquestionyouarenotsupposedtohandinsketches.Ineachpartofthisproblemyouwillconsideradecisionmaker(DM)withself-controlproblems.Inparts(a)and(b),theDMwillhavepresent-biasedpreferences.Inparticular,theDMwillhave -preferences,with beingthediscountfactorbetweentwosubsequentfutureperiodsandtheproduct beingthediscountfactorbetweenthecurrentperiodandthefirstperiodthatfollows.(a)SupposeinthispartthataDMmustdoanunpleasanttaskeitherinperiod1,inperiod2orinperiod3.Theutilitycostisincreasingwithtime,sothatitis3ifthetaskisdoneinperiod1,6ifthetaskisdoneinperiod2and8ifthetaskisdoneinperiod3.Hence,theDMisfacedwiththechoicebetween:
Doingthetaskinperiod1:Doingthetaskinperiod2:Doingthetaskinperiod3:
Assumethat,inperiod1,theDMisindifferentbetweenthesethreealternatives.Onthisbasisyouwillbeabletocalculatethat equals 9/12=3/4 (0,1/12,2/12=1/6,3/12=1/4,4/12=1/3,5/12,6/12=1/2,7/12,8/12=2/3,9/12=3/4,10/12=5/6,11/12,1)andthatequals 8/12=2/3 (0,1/12,2/12=1/6,3/12=1/4,4/12=1/3,5/12,6/12=1/2,7/12,8/12=2/3,9/12=3/4,10/12=5/6,11/12,1).IftheDMdoesnotdothetaskinperiod1,thenherpreferencesinperiod2isgivenby:Doingthetaskinperiod3isbetterthandoingthetaskinperiod2 (Doingthetaskinperiod2isbetterthandoingthetaskinperiod3,Doingthetaskinperiod3isbetterthandoingthetaskinperiod2)
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1 9 4 8 6 5 7Attachingsketchestothisquestion?Usethefollowingcode:
Inparts(b)and(c)below,considertwootherDMswhocanwatchone(andonlyone)filmoutofthreepossiblefilms:onefilmshowninperiod1,adifferentfilmshowninperiod2andthethirdfilmshowninperiod3.Thefilmshowninperiod1isacceptableandyieldsutility5.Thefilmshowninperiod2isbetterandyieldsutility7.Thefilmshowninperiod3isexcellentandyieldsutility10.Hence,thisDMisfacedwiththechoicebetween:
Watchingafilminperiod1:Watchingafilminperiod2:Watchingafilminperiod3:
(b)AssumeinthispartthattheDMhas -preferenceswith and .ThepreferencesoftheDMinperiod1is:Watchinginperiod3isbetterthanwatchinginperiod1whichisbetterthanwatchinginperiod2
(Watchinginperiod1isbetterthanwatchinginperiod2whichisbetterthanwatchinginperiod3,Watchinginperiod1isbetterthanwatchinginperiod3whichisbetterthanwatchinginperiod2,Watchinginperiod2isbetterthanwatchinginperiod3whichisbetterthanwatchinginperiod1,Watchinginperiod2isbetterthanwatchinginperiod1whichisbetterthanwatchinginperiod3,Watchinginperiod3isbetterthanwatchinginperiod1whichisbetterthanwatchinginperiod2,Watchinginperiod3isbetterthanwatchinginperiod2whichisbetterthanwatchinginperiod1)ThepreferencesoftheDMinperiod2,giventhathedidnotwatchafilminperiod1,is:Watchinginperiod2isbetterthanwatchinginperiod3 (Watchinginperiod2isbetterthanwatchinginperiod3,Watchinginperiod3isbetterthanwatchinginperiod2)IftheDMisnaïve,thenhewillwatchthefilminperiod 2 (1,2,3)IftheDMissophisticated,thenhewillwatchthefilminperiod 1 (1,2,3)IftheDMissophisticated,then,inperiod1,heiswillingtopayupto 1.0 (0,0.2,0.4,0.6,0.8,1.0,1.2,1.4,1.6,1.8,2.0,2.2,2.4,2.6,2.8,3.0,3.2,3.4,3.6,3.8,4.0)foracommitmentdevicethatmakesoneofthelaterfilmsunavailable.(c)AssumeinthispartthattheDMtakesdecisionsaccordingtothedual-selfmodel,wheretheDMisdividedintoalong-termplannerandasequenceofthreeshort-termdoers,oneforeachperiod.Ineachperiod,theplannercontrols,atacost,thedoercorrespondingtothisperiod.Assumethatthecontrolcostineachperiodis timesthedifferencebetweenthehighestpossibleutilityamongthealternativesthatremainandtheactualutility.Furthermore,assumethattheDMseekstomaximizetheundiscountedsumoftheutilities,afterthecontrolcostshavebeensubtracted,overthethreeperiods.ThenthepreferencesoftheDMis:Watchinginperiod3isbetterthanwatchinginperiod2whichisbetterthanwatchinginperiod1
(Watchinginperiod1isbetterthanwatchinginperiod2whichisbetterthanwatchinginperiod3,Watchinginperiod1isbetterthanwatchinginperiod3whichisbetterthanwatchinginperiod2,Watchinginperiod2isbetterthanwatchinginperiod3whichisbetterthanwatchinginperiod1,Watchinginperiod2isbetterthanwatchinginperiod1whichisbetterthanwatchinginperiod3,Watchinginperiod3isbetterthanwatchinginperiod1whichisbetterthanwatchinginperiod2,Watchinginperiod3isbetterthanwatchinginperiod2whichisbetterthanwatchinginperiod1)Inperiod1,theDMiswillingtopayupto 0.0 (0.0,0.2,0.4,0.6,0.8,1.0,1.2,1.4,1.6,1.8,2.0,2.2,2.4,2.6,2.8,3.0,3.2,3.4,3.6,3.8,4.0)foracommitmentdevicethatmakesoneofthelaterfilmsunavailable.
PartiallyCorrect.24of30marks.
3(a) Question3.a
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7 4 0 3 4 1 2Attachingsketchestothisquestion?Usethefollowingcode:
(5points)Inthisquestionyoucanhandinsketches.Usethesketchingpaperhandedtoyouintheexaminationvenue.Seeinstructionsonyourdesk.Pointoutmajordifferencesbetweeninequalityaversion(asspecifiedbyFehrandSchmidt1999,coursereadinglist)andreciprocalpreferences.Fillinyouranswerhereand/oronsketches
Inequalityaversion:Ui=xi-ai*max{xj-xi,0}-ßi*max{xi-xj,0}
Eninequalityaversepersonfårnyttegjennomsinmateriellepayoff(x),mensåmodereresdenpayoffenavtoleddsomharmedhvordanulikhetener.Personenfårmindrenyttedersomdeterfordelaktigulikhet(beta-leddet),ogpersonenfårmindrenyttedersomdeterufordelaktignytte(alfa-leddet),hvoralfa>beta,slikatufordelaktignytteharsterkereinnvirkningpåpersonen.Inequalityaversionfangerimidlertidkunopputfall-hvormyemanfaktiskfår,oghvormyemanfårrelativttildeandrepersonene.Reciprocalpreferencesfangerogsåopputfall-denfaktiskepayoffen.Menigjenmodererespayoffenmedetannetledd(sidendetdukkeroppiforbindelsemedsenereoppgaver,skriverjegdetikkeinnher).Nyttenmanfårblirpåvirketavhvor"snill"andreermotdeg.Enreciprocalpersonvilfåøktnytteavågjengjeldesnillhetmedsnillhetoguvennlighetmeduvennlighet.Ogbaserersegpåhvilkebeliefsmanharomhvadenandregjør.Såhererdetikkebareutfallenesombetyrnoe,menogsåhvilketankermanharomintensjonenetildeandre.Dettefangesoppvedatpersonenimodellenmedreciprocalpreferenceskanpåvirkehvilketfortegndetmodererendeleddetfår.Dersompersonenersnillmotensomersnill,fårmantopositiveleddmultiplisertmedhverandre,slikatnyttenfårenbonusavatdeersnillemothverandre.Mensdersompersonenersnillmotenslem,fårmanetpositivtogetnegativtleddmultiplisert,slikatutgangsnyttenreduseresavatdeikkebehandlerhverandrelikt.Detbetyrogsåatensomerslemmotensomerslemgirtonegativemultiplisert,somogsåblirpositiv.Slikatenpersonkanøkenyttenvedåværeslemmotensomerslem.Detteavhengernaturligvisavhvordanmandefinererkindness,menslikmodellener,handlerdetomhvormyenyttemansikrerdenandrevedsittvalgavstrategi-gittsinebeliefsomhvadenandrekommertilågjøre,oghvadenandretror.
Answered.
3(b) Question3.b(5points)
Inthisquestionyoucanhandinsketches.Usethesketchingpaperhandedtoyouintheexaminationvenue.Seeinstructionsonyourdesk.
ProvideatleastoneexampleofbehaviorthatmaybeconsistentwithbothFehr-Schmidtinequalityaversionandreciprocalpreferences,butinconsistentwithpurelyself-interestedbehavior.
Fillinyouranswerhereand/oronsketches
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1 2 2 6 6 2 1Attachingsketchestothisquestion?Usethefollowingcode:
Fillinyouranswerhereand/oronsketches
Dakanviforeksempelseforossetultimatumgame,ogenproposersomtilbyrresponderenenandels=0,2avdentotalesum.Dersomresponderenerself-interested,villehanakseptertforslagetsiden0,2>0.Personermedinequalityaverseogreciprocalpreferencesvilimidlertidkunneavslåforslaget.Inequalityaverse:Ui=xi-ai*max{xj-xi,0}-ßi*max{xi-xj,0}
s=0,2betyratresponderenfårbetydeligmindreennproposeren.Detbetyratxj-xiblirstor.Vikantenkeossatnyttentilresponderenblirlik0dersomhanavslårforslaget.Sådersomnyttenvedåaksepteres=0,2blirmindreenn0,vileninequalityaversepersonavslåforslaget.Ognyttenblirmindreenn0dersom:ai*(xj-xi)>xi
Altså.dersomdenmaterielleforskjellenmellomdetopersoneneerstornok,ogresponderensgradavufordelaktiginequalityaversionerstornok,vilresponderenhelleravslåforslagetennågodtaåfå0,2s.Reciprocalpreferences:Enreciprocalresponderviltaibetraktningintensjonenetilproposeren-omproposerenvarsnillellerusnill/slem.Ihvilkengradresponderenserpåproposerensomsnillavhengeravhvormyeproposerengirresponderensammenlignetmedhvormyeproposerenkunnegittresponderen.Igjenkanvisepånyttenvedåavslåforslagetsom0.Ogsålengenyttenavågodtaforslagetermindreenn0,vilpersonenavslådet.Oghvordanblirnyttenunder0?Jodetblirdenidettetilfellletdersomdenmateriellepayoffen,0,2s,ermindreenn"reciprocality"-leddet.Sånnnyttefunksjonenserut,fårpersonennyttegjennompayoffenhanmottar,mensåleggesdettiletleddsomblirpositivtellernegativtavhengigavhvorvidtpersoneneersnilleellerslemmemothverandre,ellervelgermotsattestrategier.Hviss=0,2blirsettpåsomslemtidettetilfellet-sidendetergodtunderforeksempel0,5,hvorbeggefårlikemye-vildenenestemåtenforpersonenågjørereciprocality-leddetpositivtpåværeåværeslemtilbake-altsååtakkeneitilforslaget.Merspesifikthandlerdetomhvormyepengerproposerensikrerrespondereniforholdtilsnittmengdensomermuligåsikreresponderen.Så0,2ergodtunder0,5-snittet.Ogdafårresponderenmulighetentilåsikreproposeren0,8(godta)eller0(avslå).Såhvisalfa-leddetinyttefunksjonenunderreciprocalpreferenceserstornok,ogforslagettilproposerenerlavtnokiforholdtilsnittet,vildetkunneværelønnsomtforenreciprocalpersonåtakkeneitilforslaget.Forellerskanhanfånegativnytte(væresnillmotenslemermindrelønnsomtennpengesummenhanmottar).
Answered.
3(c) Question3.c(5points)
Inthisquestionyoucanhandinsketches.Usethesketchingpaperhandedtoyouintheexaminationvenue.Seeinstructionsonyourdesk.
Provideatleastoneexampleofbehaviorthatisconsistentwithreciprocalpreferences,butnotwithFehr-Schmidtinequalityaversion.
Fillinyouranswerhereand/oronsketches
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5 4 8 9 7 1 6Attachingsketchestothisquestion?Usethefollowingcode:
Fillinyouranswerhereand/oronsketches
Foreksempeletultimatumgame,hvorproposerenfårmulighetentilågiresponderenentenenshares=0,1ellers=0,2avdentotalepengesummen.Laosssiatproposerengirs=0,2.Imodellenmedreciprocalpreferencesvildetsespåsom"snilt"ågis=0,2sidendetsammenlignesmed0,1.0,2ermyerelativttil0,1,ogdetvilidennemodellenkunnebligjengjeldtmedåaksepteretilbudet.Imodellenmedinequalityaversionvilimidlertiddettetilbudetkunnebliavslåttavresponderen.Intensjonenebetyringenting,såresponderenvilværelikegyldigtilatproposerenforeslodenandelensomvarhøyest.Responderenbryrsegkunomatdeterstorforskjellpåhvorstorandeldetopersonenemottaravdentotalesummen.Hvorvidtresponderenavslårellerikkeavhengeravalfa-leddetinyttefunksjonen,somtarforsegihvilkengradnyttentilresponderenlarsegpåvirkeavufordelaktigulikhet.
Answered.
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(a) Question4.a(10points)Inthisquestionyoucanhandinsketches.Usethesketchingpaperhandedtoyouintheexaminationvenue.Seeinstructionsonyourdesk.If =0and =2,whatarethefairnessequilibrium/equilibriaintheabovegame,ifany?Explain.
Fillinyouranswerhereand/oronsketches
4 Considerthefollowinggame:
Sandvika OsloCity
Sandvika 2,2 0,0
OsloCity 0,0 2,2
Thematrixdescribesthematerialpayoffsofacouple,AandB,whohaveagreedtomeetataspecifictimetodotheirjointChristmasshopping.AhassuggestedthattheymeetatSandvika,BhassuggestedthattheymeetatOsloCity.EachhasSandvikaandOsloCityastheiralternativestrategies.Eachmeetingplaceisequallygoodforbothplayersintermsofmaterialpayoffs,butiftheygodifferentplaces,noneofthemgetsanymaterialpayoffatall.Sincetheyhaverecentlyhadanunpleasantfight,eachisawarethattheothermightbeangry.
LetUidenotei'sutility,whilexidenotesi'smaterialpayoff(whichwilldependonplayers'strategies).Assumethateachi=A,Bhaspreferencesasspecifiedbelow:
(i)
where kindnesstowardsj, kindnesstowardiaccordingtoi'sbelief(i=1,2;j=1,2;.Further,let
(ii)
(iii)
wheresi=i'sstrategy,bij=i'sbeliefaboutj'sstrategy, isthelargestmaterialpayofficouldsecuretoj,
giveni'sbeliefaboutj'sstrategybij,while isthesmallestmaterialpayofficouldsecuretoj,givenbij.Finallyciji=i'sbeliefaboutj'sbeliefabouti'sstrategy.
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11/171 8 7 5 0 3 7Attachingsketchestothisquestion?
Fillinyouranswerhereand/oronsketches
Somutregning1påtegnearketviser,er:U1(s,s)=2U2(s,s)=4Dersomdetskalværeetfairnessequilibrium,mådetværeulønnsomtforenellerbeggeavdemåskiftetaktikk.DerforkanvistartemedåsjekkeU1(o,s):Utregning2viseratU1(o,s)=00<2,sådetvilikkeværelønnsomtforperson1åskiftetaktikktilåmøteoppvedOslocity-gittbeliefsomatdenandremøteroppiSandvika.Sålengedetsammegjelderforperson2,vils,sværeetfairnessequilibrium.Dettekanvisjekkenå:Utregning3viseratU2(s,0)=-2-2<4,sådetvilikkeværelønnsomtforperson2åskiftetaktikkåmøteoppvedOslocity-gittbeliefsomatdenandremøteroppiSandvika.Altsåer(s,s)etfairnessequilibrium.Sidensituasjoneneridentiskmed(o,o)somutgangspunkt,betyrdetatogså(o,o)eretfairnessequilibrium.Hvasåmed(o,s)og(s,o)?Deblirogsåidentiske,sådetholderatvistudererenavdem.Vikansepå(o,s):U1(o,s)=0Vildetlønnesegforperson1ådeviate,gitthansbeliefsomdenandresstrategi?Vivetathanfårnytte2dersombeggevelgerlikstrategi,detbetyratdersomhanskifterfraotils,vilhanfånytteU2(s,s)=2Altsåkanikke(o,s)væreetfairnessequilibrium.Ogtilsvarendemekanismegjelderfor(s,o).Konklusjon:(o,o)og(s,s)erfairnessequilibrium.Hvorfor?Person1harikkereciprocalpreferences,hanbryrsegkunomsinprivatenytte(bryresgikkeomdenandresintensjonerpgaalfa=0).Såhanønskeråoppnådenstrategiensomgirhanmestnytteisegselv.Detvilderforaldrigimeningåskiftestrategifrasdersomhantrorperson2kommertilåspilles,ogdetsammemedo.Person2harreciprocalpreferences,åønskerågjengjeldegodeintensjonermedkindnessogdårligeintensjonermedunkindness.Menidettetilfelletvildetegneltiguansettlønnesegågjøredetperson1gjør.Fordavilhanbådetilfredsstilledereciprocalpreferenceshanhar,oghanvilfåstørrepayoffisegseg(altsåuavhengigavalfa-leddet).
Answered.
ECON42601BehavioralEconomics Candidate172504
12/17
1 8 7 5 0 3 7Attachingsketchestothisquestion?Usethefollowingcode:
ECON42601BehavioralEconomics Candidate172504
13/17
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(b) Question4.b(7.5points)
ECON42601BehavioralEconomics Candidate172504
14/17
3 7 1 3 1 9 0Attachingsketchestothisquestion?Usethefollowingcode:
Inthisquestionyoucanhandinsketches.Usethesketchingpaperhandedtoyouintheexaminationvenue.Seeinstructionsonyourdesk.If ,is(Sandvika,Sandvika)afairnessequilibriumintheabovegame?Explain.Fillinyouranswerhereand/oronsketches
Somutregning1viser,blirnyttentildetopersonenegittstrategi(s,s):u1=4u2=4Foratdetskalværeetfairnessequilibrium,mådetværeulønnsomtforbeggetoåskiftestrategi:Utregning2viseratnyttentilperson1dersomhanskiftertaktikkblirU1(o,s)=-2Utregning3viseratnyttentilperson2dersomhanskiftertaktikkblirU2(s,o)=-2Altsåvilingenhagodtavåskiftetaktikk,ogaltsåer(s,s)etfairnessequilibriumBeggeharreciprocalpreferences,ogvilgjengjeldekindnessmedkindnessogunkindnessmedunkindness.Mendetvilaldriværelønnsomtåspillemotsattavdetdenandregjør.Fordatrormandenandreviserkindness,menmanvelgerlikevelågjengjeldedetmedunkindness.Noesombådegirlaverepayoffisegselv(gårfra2til0),ogdetgjøratmanikkelengerfårtilfredsstiltsinereciprocalpreferences,hvilketgjøratpayoffenfaktiskblirendalavere,-2istedetfor0.
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ECON42601BehavioralEconomics Candidate172504
15/17
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(c) Question4.c(7.5points)
ECON42601BehavioralEconomics Candidate172504
16/17
9 3 3 4 9 4 6Attachingsketchestothisquestion?Usethefollowingcode:
Inthisquestionyoucanhandinsketches.Usethesketchingpaperhandedtoyouintheexaminationvenue.Seeinstructionsonyourdesk.If is(Sandvika,OsloCity)(i.e.AgoestoSanvika,whileBgoestoOsloCity)afairnessequilibriumintheabovegame?Explain.Fillinyouranswerhereand/oronsketches
Utregning1viseratnyttentilperson1understrategisandvika,gittbeliefsomatperson2spilleroslo,oggittbeliefomatperson2vetatperson1vilspillesandvika:u1(s,o)=2Utregning2viseratnyttentilperson2understrategioslo,gittbeliefsomatperson1spillersandvika,oggittbeliefsomtaperson1vetatperson2vilspilleoslo:u2(s,o)=2Foratdetskalværeetfairnessequilibrium,mådetaltsåværeulønnsomtåskiftetaktikkUtregning3viseratnyttentilperson1vedåskiftefrastilo,gittbeliefsomatperson2spillerosamtidigsomperson2troratperson1skalspilles:U1(o,o)=0Utregning4viseratnyttentilperson2vedåskiftefraotils,gittbeliefsomatperson1spilleroogatperson1trorperson2kommertilåspilles:u2(s,s)=0Altsåer(S,O)etfairnessequilibriummeddissereciprocalpreferences.Defåraltsåbeggetolaverepayoffisegselv.Menreciprocalpreferences(altsåalfa-leddet)gjøratdetikkeerdetenestesombetyrnoe.Siden1tror2harrettebeliefsomhva1kommertilågjøre,menlikevelvelgerågjøremotsatt-altsåviseunkindness-vildetværemerlønnsomtforperson1åværeunkindtilbake,ennåfølgeperson2sittvalgforåfåpayoff2.Fornårmantrekkerinnreciprocal-leddet,blirdenpayoffen0istedet.Ogdensammetankegangengjelderogsåforperson2.
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ECON42601BehavioralEconomics Candidate172504
17/17
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