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1、14.127Lecture4XavierGabaixFebruary26,20041BoundedRationalityThreereasonstostudy:•Hopethatitwillgenerateaunifiedframeworkforbehavioraleconomics•Somephenomenashouldbecaptured:difficulteasydifference.Itwouldbegoodtohaveametricforthat•ArtificialintelligenceWarning—alotofeffortspendonboundedrationalitysince
2、Simonandfewresults.Threedirections:•Analyticalmodels—Don’tgetallthefinenuancesofthepsychology,butthosemodelsaretractable.•Processmodels,e.g.artificialintelligence—Rubinsteindirection.SupposeweplayNash,givenyourreactionfunction,mystrategyoptimizesonbothoutcomeandcomputingcost.Rubinsteinprovessomeexi
3、stencetheorems.Butitisverydifficulttoapplyhisapproach.•Psychologicalmodels—Thosemodelsaredescriptivelyrich,buttheyareunsystematic,andoftenhardtouse.Humancomputercomparison•Humanmind1015operationspersecond•Computer1012operationspersecond•Moore’slaw:every1.5yearscomputerpowerdoubles•Thus,every15years
4、computerpowergoesup103•Ifwebelievethis,thenin45yearscomputerscanbe106morepowerfulthanhumans•Ofcourse,we’llneedtounderstandhowhumanthink1.1Analyticalmodels•BoundedRationalityasnoise.Consumerseesanoisysignalq˜=q+σεofquantity/qualityq.•BoundedRationalityasimperfectmonitoringofthestateoftheworld.Peop
5、ledon’tthinkaboutthevariablesallthetime.Theylookupvariablekattimest1,...,tn•BoundedRationalityasadjustmentcost.Callbyθtheparametersoftheworld.—NowIamdoinga0andκ=costofdecision/change—Ichangemydecisionfroma0toa∗=argmaxu(a,θt)iffu(a∗,θt)−u(a0,θt)>κ1.1.1ModelofBoundedRationalityasnoise•Randomutilitym
6、odel—Luce(psychologist)andMcFadden(econometricianwhoprovidedeconometrictoolsforthemodels)—ngoods,i=1,...,n.—Imaginetheconsumerchoosesmaxqi+σiεii—What’sthedemandfunction?•Definition.TheGumbeldistributionGis−e−xF(x)=P(ε0,wher
7、eγ≃0.59istheEulerconstant.•Proposition1.SupposeεiareiidGumbel.Then��∗−e−xPmaxεi+qi≤lnn+q+x=ei=1,..,nwithq∗definedaseq∗=1�eqi.ThismeansthatnMd∗n=maxεi+qi=lnn+q+ηi=1,..,nandηisaGumbel.ProofofProposition1.��•CallI=Pmaxi=1,
