06 Nash equilibrium dating and Cournot.docx
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06 Nash equilibrium dating and Cournot.docx
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06NashequilibriumdatingandCournot
GameTheory:
Lecture6Transcript
Overview:
WeapplythenotionofNashEquilibrium,first,tosomemorecoordinationgames;inparticular,theBattleoftheSexes.ThenweanalyzetheclassicCournotmodelofimperfectcompetitionbetweenfirms.Weconsiderthedifficultiesincolludinginsuchsettings,andwediscussthewelfareconsequencesoftheCournotequilibriumascomparedtomonopolyandperfectcompetition.
September24,2007
< ProfessorBenPolak: Allright,solasttimeweweretalkingaboutTheInvestorGameandthiswasacoordinationgame,andwelearnedsomethings.IjustwanttorecallsomeofthethingswelearnedsoIcanhighlightthemabit.Onethingwelearnedwasthatcommunicationcanhelpinacoordinationgame.SoIforgetwhoitwas,butsomeonedownherewhohasdisappeared,wasourJimmyStewartcharacterandhelpedcoordinateyouonabetterequilibriumsimplybysuggestingwhatyoushoulddo. Therearetwolessonshere.OneisthisisverydifferentfromthePrisoner'sDilemma.SowelearnedtheveryfirsttimethatinthePrisoner'sDilemmacommunicationpersewon'thelp,butinthecoordinationproblem,whichcouldbejustasserioussociallyasaPrisoner'sDilemma,inacoordinationproblemitmaywellhelp.Thereasonithelpsisyou'retryingtocoordinateontoaNashEquilibrium.OnewaytothinkaboutNashEquilibriaisthattheyareself-enforcingagreements,soprovidedthateveryonebelievesthateveryoneisgoingtogoalongwiththisagreement,theneveryoneinfactwill. Iwanttomakeanother,slightlymorephilosophicalremarkassociatedwiththisandit'stodowiththeideaof"leadership."Soleadershipiskindofabigwordthatyouseewrittenprobablytoooftenthesedays,intoomanynewspaperarticles,anditprobablycomesupintoomanyYaleclasses,andIdon'tclaimtoknowanythingaboutleadership.AndIdon'tthinkGameTheoryisgoingtocontributetoanythingtounderstandingaboutleadership.Butonethingwecandoistellyouwhereleadershipmayhelp.Inthecoordinationgame,wheretheideaistotryandgetpeopletocoordinateonaparticularequilibriaratherthanonanotherequilibria,orworsestill,tobeuncoordinatedentirely.Inthosekindofgames,leadershipcanhelptremendously.Alittlebitofleadershipcanhelptremendously.Sothesegames,thesecoordinationgames,aregameswherethereisa"scopeforleadership." Justtoseethatinaverysimpleexample,again,wedon'tusesuchacomplicatedexampleastheonewelookedatlasttime,youcouldimagineagame,areallytrivialcoordinationgame,whichlookedlikethis(1,1)(0,0)(0,0)(1,1).Andclearlyinthisgamewhatmattersiscoordinating.Youeitherwanttocoordinateonupleftoryouwanttocoordinateondownright.Youdon'twanttoendupuncoordinatedondownleftorupright.Everyoneseethat? Sointhisgameifyoujustplayedit,it'squitelikelyyou'regoingtoendupuncoordinated,butifyouhavealittlebitofleadershipcansayokaylet'smakesurethisiswherewecoordinate,orlet'smakesurethisiswherewecoordinate.Sothismattersalot.AndIdon'twanttooverplaythesocialimportanceofthis,butgobackacoupleofyearstowhatwashappeningintheaftermathofKatrinaandrealizehowimportant--howbadthingsgetwhenthingsfailtobecoordinated. Oneotherremarkbeforeweleavethis,inthegameweplayedlasttime,intheinvestmentgame,onefeatureofthatgamewasthatthemoreyouthoughtotherpeopleweregoingtoinvest,themoreyouwantedtoinvest.Themoreyouthoughtotherpeopleweregoingtoinvest,themorelikelythatyouweregoingtoinvest.Ifyougobacktothetimebeforethat,wetalkedaboutthispartnershipgame.Inthepartnershipgameyouwerecontributingefforttoajointproject.Itcouldhavebeenalawfirm;itcouldhavebeenworkinginthestudygrouponahomeworkassignment. Inthatgame,ifyourememberwhatthebestresponseslookedlike,theylookedlikethiswherethiswastheeffortofPlayer1;thiswastheeffortofPlayer2.ThiswasthebestresponseofPlayer1andthiswasthebestresponseofPlayer2.Thisgamealsohasthefeaturethatthemoreefforttheotherperson--themoretheotherpersondoes--themoreyouwanttodo.Themoreeffortyourpartnerprovidesintothisprojectthemoreeffortyouwanttoprovideinthisproject.Ijustwanttointroduceabitofjargonhere.ThesegamesinwhichthemoretheotherpersondoesthemoreIwanttodo,thesearecalledgamesofstrategiccomplements.Thesearegamesofstrategiccomplements.Soboththeinvestmentgameandthegamewith--thepartnershipfirmgamearegameswithstrategiccomplements.Wecouldcallthestrategiesstrategiccomplements.We'llcomebacktothislaterontoday. Sobeforeweleavecoordinationgames,Iwanttolookatanotherone,alittlebitmorecomplicatedoneperhaps,thatwementionedbrieflylasttime.Sowe'lllookatandplayanothergame,andwe'llcallthisgame,"GoingtotheMovies."SoIalwaysregardonepurposeofthisclasstohelphaplessYalestudentsintheirdatingstrategies.Thatseemslikeagoodthingtodo.HowmanyofyouareEconmajors? There'salotofpeoplewhoprobablyneedalotofhelpwiththeirdatingstrategies,right? Okay,sotheideaofthisgameisacoupleisgoingtomeetupatthemovies.Andlet'shavealookatthemoviesconcernedhereandwe'lldraw--there'sthreepossiblemovies.Themovieswe'regoingtolookatareTheBourneUltimatum,andthemoviecalledGoodShepherd,andamoviecalledSnowWhiteandI'llexplainthegameinmoredetailinasecond. Now,itusedtobeintheolddaysbeforeIhadkids,Icouldlistoff15currentmoviesandhelpyouabitmorewithyourdatingstrategybygivingyouinstantmoviereviews,butnowIhavekids,Igettoseepreciselytwomoviesayear,andthetwomoviesIgottoseethisyearwereTheBourneUltimatumandtheGoodShepherd.AndnowIthinkaboutit,bothofthosehaveMattDamoninit.MywifechosebothsomaybeIneedtoworkoutsomemore.Sojusttogiveyousomeideaaboutthesemovies,howmanyofyousawBourneUltimatum? Quitealotofyou;thisisamovie,ithasprettygoodaction,virtuallynoplot.Basiclessonofthismovieis--ifyoutakehomealesson--it'sthatallspiesarepsychosorsomethinglikethat. ThenhowmanyofyousawGoodShepherd? Alotofyousawthataswell.It'sactuallyprettygood.Ithasalotofplotandnoaction,soit'stheotherwayaround.Thebasiclessonofthismovieis--andyouprobablyknewthisalready--everyoneatYaleisaspy…andbythewayalsoapsycho.ThethirdmovieisSnowWhite,whichIhaven'tgoneouttoseebutmyfour-yearolddaughterhasseenon24ofthelast27nightsonvideo.Andthismovie,Idon'tknowifIwouldrecommenditthatmuch,it's--perhapsI'mbeingtooPC--butI'mnotconvincedthatforthemodernwoman,hangingaroundwaitingforyourprincetocomeisreallyagoodstrategy.Bytheway,forthoseofyou--thoseofyouwhoare,ifyouaredoingthatstrategy,gotmeintrouble.Nevermind,ifyouaredoingthatstrategy,takeitfromaBrit,mostprincesareasdumbastoast,notworthwaitingfor. Solet'sputthepayoffsinhere.Sotheideahereisthatthesepeoplearegoingtomeetatthemovie,they'regoingtogoouttoamovie.Andthey'vedecidedtogototheCriterion[NewHavenmovietheatre],orthelocalmoviehouse,andtherewerethesethreemoviesshowing,andthey'reallexcitedaboutgoingtothismovieexceptbeingEconomicsmajorsandnotverygoodatdating,theyhaveforgottentotelleachotherwhichmoviethey'reactuallygoingtogoto.They'regoingtomeetinthereonthe--inthebackrowprobablyand--butthey'renottellinguswhichmovie.Sothat'saproblemandlet'sputinthepayoffs,andwe'llputinthepayoffsthatroughlyIthinkwouldcorrespond--somypreferencesandwe'lltalkaboutit--whatthesepreferencesmeaninasecond. Soherewegoso…-1,(-1,0),(-1,0),(-2,-2).SoherearethepreferencesforthesemoviesofPlayer1andPlayer2,andyoucanseefromthesepreferences,fromthesepayoffs,thatthebestthingforPlayer1isforbothplayers,bothpeopletomeetandgototheBourneUltimatum;thisistheactionmovie.Soit'snottobesexist--assumethisisthesheandthisisthehe,soshewouldliketogoandseeMattDamonbeatpeopleupandcoordinateonthat,herfavoritething.Andshegetsnothingiftheyfailtocoordinateandsoonandsoforth.HersecondchoiceistomanagetocoordinateatMattDamonbeingaYalespy,andthenshereallydoesn'twanttogoandseeSnowWhite,andtheworstthingofall,actuallythisisforbothplayers,theworstthingofallistocoordinatewithSnowWhitebecausethenyou'vegottotalkaboutitafterwardsatKoffee[NewHavencafé]. Samethingwiththeotherperson.Samethingexactly,exceptthathewouldrathermeetattheGoodShepherd.Sincehe'saYaleguy,heprobablythinksofhimselfastheMattDamoncharacterthoughperhapsnot,andfailingthat,he'dliketocoordinateattheBourneUltimatum.Butagain,thedisasteristofailtocoordinateandgotoseedifferentmovies.Sothesearethepreferences.Whatcanwetellimmediately,ifyou'restuckinthissituation? Whatcanyoutellimmediatelyaboutthisgame? What'saneasyfirststep? Let'sgettheguyintheredhere. Student: SnowWhiteisdominatedbybothplayers. ProfessorBenPolak: Good,soforbothplayersSnowWhiteisadominatedstrategy.Sobothplayershavingtakenthisclass--Itoldyouitwouldhelpyouwithyourdating.SobothplayerswillrealizethattheyshouldatleastnotgotoSnowWhite,isthatright? Greatanimationbutnotperhapsa
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