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1、Marketefficiency,anticipationandtheformationofbubbles-crashesSergeGalam∗,CentredeRechercheenEpist´emologieAppliqu´ee,´EcolePolytechniqueandCNRS,´CREA,BoulevardVictor,32,75015Paris,FranceMarch19,2018AbstractAdynamicalmodelisintroducedfortheformationofabullishorbearishtrendsdrivinganassetpric
2、einagivenmarket.Initially,eachagentdecidestobuyorsellaccordingtoitspersonalopinion,whichresultsfromthecombinationofitsownprivateinformation,thepub-licinformationanditsownanalysis.Itthenadjustssuchopinionthroughthemarketasitobservessequentiallythebehaviorofagroupofrandomselectionofotherage
3、nts.Itschoiceisthendeterminedbyalocalmajorityruleincludingitself.Whenevertheselectedgroupisatatie,i.e.,itisundecidedonwhattodo,thechoiceisdeterminedbythelocalgroupbeliefwithrespecttotheanticipatedtrendatthattime.Theselocaladjustmentscreateadynamicthatleadsthemar-ketpriceformation.Incaseof
4、balancedanticipationsthemarketisarXiv:1106.1577v1[physics.soc-ph]8Jun2011foundtobeefficientinbeingsuccessfultomakethe“rightprice”toemergefromthesequentialaggregationofallthelocalindividualinfor-mationswhichalltogethercontainthefundamentalvalue.However,whenaleadingoptimisticbeliefprevails,th
5、esameefficientmarketmechanismsarefoundtoproduceabullishdynamiceventhoughmostagentshavebearishprivateinformations.Themarketyieldsthenawiderandwiderdiscrepancybetweenthefundamentalvalueandthe∗serge.galam@polytechnique.edu1marketvalue,whichinturncreatesaspeculativebubble.Neverthe-less,thereexi
6、stsalimitinthegrowingofthebubblewhereprivateopinionstakeoveragainandatonceinvertthetrend,originatingasuddenbearishtrend.Moreover,inthecaseofadrasticshiftinthecollectiveexpectations,ahugedropinpricelevelsmayalsooccurex-tremelyfastandputsthemarketoutofcontrol,itisamarketcrash.Keywords:renor
7、malizationgroup,sociophysics,opiniondynamic,fi-nance21FromtheideaofeachagenttotheopinionofeveryoneInthispaper,Iapplysociophysics[1,2,3]totheanalysisoftheaggregationofopinionsinfinancialmarkets.Asimplemodelisshowntodescribethemovementofastockpricefarawayfromitsfundamen
