{"id":4021,"date":"2017-03-06T14:21:51","date_gmt":"2017-03-06T12:21:51","guid":{"rendered":"https:\/\/sbunker.org\/?p=4021"},"modified":"2024-11-18T14:26:08","modified_gmt":"2024-11-18T12:26:08","slug":"arratisja-nga-burgu","status":"publish","type":"post","link":"https:\/\/sbunker.org\/en\/uncategorized\/arratisja-nga-burgu\/","title":{"rendered":"Arratisja nga burgu"},"content":{"rendered":"
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Shkrimi i pest\u00eb nga idet\u00eb themelore t\u00eb ekonomis\u00eb zb\u00ebrthen ekuilibrin e Nash-it<\/p>\n<\/div>\n

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John Nash arriti n\u00eb Universitetin e Princeton n\u00eb vitin 1938 p\u00ebr t\u00eb filluar doktorat\u00ebn me let\u00ebr rekomandimi n\u00eb nj\u00eb fjali: \u201cAi \u00ebsht\u00eb nj\u00eb gjeni i matematik\u00ebs\u201d. Nuk zhg\u00ebnjeu. Vet\u00ebm 19 vje\u00e7ar dhe me p\u00ebrfundimin e vet\u00ebm nj\u00eb l\u00ebnd\u00eb t\u00eb ekonomis\u00eb gjat\u00eb universitetit, n\u00eb 14 muajt e par\u00eb gjat\u00eb m\u00ebsimeve t\u00eb doktorat\u00ebs ai b\u00ebri pun\u00eb t\u00eb madhe, p\u00ebr t\u00eb cil\u00ebn n\u00eb vitin 1944 do ta shp\u00ebrblenin at\u00eb me \u00e7mim Nobel p\u00ebr ekonomi, p\u00ebr kontribut n\u00eb teorin\u00eb e loj\u00ebs.<\/p>\n

M\u00eb 16 N\u00ebntor 1946, Nash d\u00ebrgoi nj\u00eb let\u00ebr jo m\u00eb t\u00eb gjat\u00eb se nj\u00eb faqe p\u00ebr Akademin\u00eb Nacionale t\u00eb Shkencave, n\u00eb t\u00eb cil\u00ebn ai shtroi nj\u00eb koncept q\u00eb m\u00eb von\u00eb do t\u00eb njihej si \u201cekuilibri i Nash-it\u201d. Ky koncept p\u00ebrshkruan nj\u00eb rezultat stabil q\u00eb vjen nga njer\u00ebzit, apo institucionet t\u00eb cil\u00ebt b\u00ebjn\u00eb zgjedhje racionale t\u00eb bazuara n\u00eb at\u00eb se \u00e7ka ata mendojn\u00eb se t\u00eb tjer\u00ebt do t\u00eb veprojn\u00eb. N\u00eb nj\u00eb ekuilib\u00ebr t\u00eb Nash-it, askush nuk \u00ebsht\u00eb n\u00eb gjendje t\u00eb p\u00ebrmir\u00ebsoj\u00eb q\u00ebndrimin e tij, \u00a0duke ndryshuar strategji: \u00e7do person \u00ebsht\u00eb n\u00eb gjendjen m\u00eb t\u00eb mir\u00eb t\u00eb mundshme, edhe n\u00eb qoft\u00eb se kjo nuk n\u00ebnkupton rezultat optimal p\u00ebr shoq\u00ebrin\u00eb. Me nj\u00eb demonstrim elegant matematikor, Nash tregoi se \u00e7do \u201cloj\u00eb\u201d me nj\u00eb num\u00ebr t\u00eb caktuar t\u00eb lojtar\u00ebve, secili me nj\u00eb num\u00ebr t\u00eb caktuar t\u00eb opsioneve p\u00ebr t\u00eb zgjedhur, do t\u00eb ket\u00eb t\u00eb pakt\u00ebn nj\u00eb ekuilib\u00ebr t\u00eb till\u00eb.<\/p>\n

Mendimet e tij zgjeruan gam\u00ebn e ekonomiksit. N\u00eb tregje t\u00eb konkurrenc\u00ebs perfekte, ku nuk ka barriera p\u00ebr hyrje n\u00eb treg dhe t\u00eb gjith\u00eb kan\u00eb produkte identike, asnj\u00eb bler\u00ebs apo shit\u00ebs nuk ka ndikim n\u00eb treg: asnj\u00ebri nuk ka nevoj\u00eb t\u2019i kushtoj\u00eb r\u00ebnd\u00ebsi t\u00eb ve\u00e7ant\u00eb se \u00e7ka jan\u00eb duke b\u00ebr\u00eb t\u00eb tjer\u00ebt. Por, shum\u00eb prej tregjeve nuk jan\u00eb t\u00eb till\u00eb: vendimet e rival\u00ebve dhe t\u00eb konsumator\u00ebve kan\u00eb r\u00ebnd\u00ebsi. Nga ankandet e deri tek tregjet e pun\u00ebs, ekuilibri i Nash-it i dha shkenc\u00ebs s\u00eb ekonomis\u00eb nj\u00eb m\u00ebnyr\u00eb p\u00ebr t\u00eb b\u00ebr\u00eb parashikime t\u00eb bot\u00ebs reale, duke u bazuar n\u00eb informacionin rreth stimujve t\u00eb secilit person.<\/p>\n

Nj\u00eb shembull n\u00eb ve\u00e7anti ka simbolizuar k\u00ebt\u00eb ekuilib\u00ebr: dilema e t\u00eb burgosurit. Nash ka p\u00ebrdorur algjebr\u00ebn dhe numrat p\u00ebr t\u00eb shpjeguar k\u00ebt\u00eb situat\u00eb n\u00eb nj\u00eb punim t\u00eb gjer\u00eb n\u00eb vitin 1951, por, versioni i njohur p\u00ebr student\u00ebt e ekonomiksit \u00ebsht\u00eb m\u00eb i mb\u00ebrthyer.<\/p>\n

P\u00ebrfshin dy kriminel\u00eb n\u00eb dy qeli t\u00eb ndryshme burgu, t\u00eb dy duke menduar p\u00ebr ofert\u00ebn e nj\u00ebjt\u00eb t\u00eb ofruar nga avokati. N\u00eb qoft\u00eb se t\u00eb dy rr\u00ebfejn\u00eb vrasjen, t\u00eb dy marrin 10 vite burg. N\u00eb qoft\u00eb se nj\u00ebri nuk flet dhe tjetri spiunon, at\u00ebher\u00eb spiuni merr shp\u00ebrblim, nd\u00ebrsa tjetri merr burgim t\u00eb p\u00ebrjetsh\u00ebm. Kurse, n\u00eb qoft\u00eb se t\u00eb dy nuk flasin, at\u00ebher\u00eb t\u00eb dy marrin d\u00ebnim t\u00eb vog\u00ebl, me vet\u00ebm nj\u00eb vit (shiko diagramin).<\/p>\n

\"Image\"<\/div>\n

\u00cbsht\u00eb vet\u00ebm nj\u00eb zgjidhje e ekulibirit t\u00eb Nash-it rreth dilem\u00ebs s\u00eb t\u00eb burgosurit: t\u00eb dy rr\u00ebfehen. Se cila \u00ebsht\u00eb p\u00ebrgjigja m\u00eb e mir\u00eb e strategjis\u00eb s\u00eb tjetrit; n\u00ebse tjetri mund t\u00eb ket\u00eb folur, spiunimi t\u00eb shp\u00ebton nga burgimi i p\u00ebrjetsh\u00ebm. Tragjedia \u00ebsht\u00eb se n\u00eb qoft\u00eb se ata do t\u00eb mund t\u00eb b\u00ebnin nj\u00eb koordinim, do t\u00eb b\u00ebnin m\u00eb t\u00eb mir\u00ebn p\u00ebr veten.<\/p>\n

Shembulli ilustron q\u00eb turmat mund t\u00eb jen\u00eb sa t\u00eb pamend, aq edhe t\u00eb men\u00e7ura; \u00e7far\u00eb \u00ebsht\u00eb m\u00eb e mira p\u00ebr nj\u00eb individ mund t\u00eb jet\u00eb shkat\u00ebrrimtare p\u00ebr grupin. Ky rezultat tragjik \u00ebsht\u00eb shum\u00eb i shpesht\u00eb n\u00eb jet\u00ebn reale. Duke i l\u00ebn\u00eb t\u00eb lir\u00eb t\u00eb peshkojn\u00eb, njer\u00ebzit mund t\u00eb z\u00ebn\u00eb m\u00eb shum\u00eb peshk, por sa \u00ebsht\u00eb e mir\u00eb \u00a0kjo p\u00ebr grupin, duke zbrazur stoqet e peshkut. \u00a0Pun\u00ebtor\u00ebt n\u00eb gar\u00eb p\u00ebr t\u00eb impresionuar shefin duke ndenjur m\u00eb gjat\u00eb n\u00eb zyr\u00eb inkurajojn\u00eb rraskapitjen e fuqis\u00eb s\u00eb tyre. Bankat kan\u00eb nj\u00eb stimul p\u00ebr t\u00eb dh\u00ebn\u00eb borxh m\u00eb shum\u00eb kur \u00e7mimet e sht\u00ebpive rriten.<\/p>\n

Problemi i turmave<\/strong><\/p>\n

Ekuilibri i Nash-it u ka ndihmuar ekonomist\u00ebve q\u00eb t\u00eb kuptojn\u00eb sesi rritja individuale mund t\u00eb \u00e7oj\u00eb n\u00eb d\u00ebmtim t\u00eb turmave. Kjo ka ndihmuar t\u00eb trajtohet nj\u00eb problem: thjesht duhej t\u00eb siguroheshin q\u00eb \u00e7do individ p\u00ebrballet me stimulim m\u00eb t\u00eb mir\u00eb t\u00eb mundsh\u00ebm. N\u00eb qoft\u00eb se gj\u00ebrat prap\u00ebseprap\u00eb shkojn\u00eb keq \u2013 t\u00eb themi, prind\u00ebrit d\u00ebshtojn\u00eb t\u00eb vaksinojn\u00eb f\u00ebmij\u00ebt kund\u00ebr fruthit \u2013 at\u00ebher\u00eb kjo mund t\u00eb jet\u00eb p\u00ebr shkak se njer\u00ebzit nuk ishin duke vepruar n\u00eb interes t\u00eb vetvetes. N\u00eb raste t\u00eb tilla, sfida e politikave publike do t\u00eb ishte e sojit t\u00eb informacionit.<\/p>\n

Ideja e Nash-it kishte paraardh\u00ebs. N\u00eb vitin 1838, August Cournot, ekonomist francez, dha teorin\u00eb se n\u00eb nj\u00eb treg me vet\u00ebm dy kompani n\u00eb konkurrenc\u00eb, secila do t\u00eb shoh\u00eb disavantazhet e ndjekjes s\u00eb pjes\u00ebs s\u00eb tregut duke e nxitur output-in, n\u00eb form\u00ebn e \u00e7mimeve t\u00eb ul\u00ebta dhe profiteve margjinale m\u00eb t\u00eb dob\u00ebta. Pa dashje, Cournot kishte ngecur n\u00eb nj\u00eb shembull t\u00eb ekuilibrit t\u00eb Nash-it. Kishte kuptim p\u00ebr \u00e7do firm\u00eb q\u00eb t\u00eb vendoste nivelet e prodhimit t\u00eb bazuara n\u00eb strategjin\u00eb e konkurrentit t\u00eb tij; konsumator\u00ebt, do t\u00eb p\u00ebrfundonin me m\u00eb pak gj\u00ebra dhe me \u00e7mime m\u00eb t\u00eb larta sesa po t\u00eb zhvillohej nj\u00eb treg i rregullt.<\/p>\n

Nj\u00eb tjet\u00ebr ishte John von Neumann, nj\u00eb matematikan hungarez. N\u00eb vitin 1928, kur Nash kishte lindur, von Neumann p\u00ebrshkroi teorin\u00eb e par\u00eb formale t\u00eb loj\u00ebs, duke treguar se mes dy personave, n\u00eb loj\u00ebn humb\u00ebs-fitues, gjithmon\u00eb do t\u00eb ket\u00eb nj\u00eb ekuilib\u00ebr. Kur Nash ndau t\u00eb gjeturat e tij me von Neumann, at\u00ebher\u00eb ishte matematikan i shquar, ky i fundit tha se rezultatet ishin t\u00eb par\u00ebnd\u00ebsishme, duke e par\u00eb at\u00eb si zbulim t\u00eb tij, vet\u00ebm se version m\u00eb i zgjeruar.<\/p>\n

N\u00eb fakt, fokusi i von Neumann n\u00eb dy persona dhe loja humb\u00ebs-fitues la vet\u00ebm disa aplikime t\u00eb ngushta t\u00eb teoris\u00eb s\u00eb tij. Shum\u00eb prej tyre ishin t\u00eb natyr\u00ebs ushtarake. E till\u00eb ishte ideja e shkat\u00ebrrimit reciprok t\u00eb p\u00ebrbashk\u00ebt, n\u00eb t\u00eb cil\u00ebn ekuilibri arrihet duke armatosur kund\u00ebrshtar\u00ebt me arm\u00eb nukleare (disa kan\u00eb th\u00ebn\u00eb se karakteri filmik Dr. Strangelove ishe i bazuar n\u00eb von Neumann). Asnj\u00eb prej k\u00ebtyre nuk ishte e dobishme p\u00ebr t\u00eb menduarit rreth situatave \u2013 p\u00ebrfshir\u00eb shum\u00eb prej llojeve t\u00eb tregjeve \u2013 n\u00eb t\u00eb cil\u00ebn fitorja e nj\u00ebr\u00ebs pal\u00eb nuk implikon automatikisht humbjen e tjetrit.<\/p>\n

Megjithat\u00eb, fillimisht profesioni i ekonomiksit p\u00ebrdori iden\u00eb e von Neumann-it, dhe e shikoi me holl\u00ebsi zbulimin e Nash-it. Ai vazhdoi karierr\u00ebn n\u00eb k\u00ebrkime t\u00eb reja matematikore, por shpresat e suksesit t\u00eb tij u shuan kur n\u00eb vitin 1959 filloi t\u00eb vuaj\u00eb nga iluzionet dhe paranoja. Gruaja e tij e shtroi n\u00eb spital; pasi doli prej tij, ai u b\u00eb nj\u00eb figur\u00eb e njohur n\u00eb kampusin e Princeton, duke folur me veten dhe duke shkarravitur n\u00eb d\u00ebrras\u00eb t\u00eb zez\u00eb. Teksa p\u00ebrballej me sh\u00ebndetin e tij t\u00eb dob\u00ebt, ekuilibri i tij dita-dit\u00ebs b\u00ebhej m\u00eb i r\u00ebnd\u00ebsish\u00ebm p\u00ebr disiplin\u00ebn. Numri i studimeve\/hulumtimeve q\u00eb cituan ekuilibrin e Nash-it u rrit p\u00ebr shtat\u00eb her\u00eb q\u00eb nga viti 1980, dhe koncepti \u00ebsht\u00eb p\u00ebrdorur p\u00ebr t\u00eb zgjidhur probleme politikave t\u00eb bot\u00ebs reale.<\/p>\n

Nj\u00eb shembull i famsh\u00ebm ishte sistemi spitalor amerikan, q\u00eb n\u00eb vitin 1940 ishte n\u00eb ekuilib\u00ebr t\u00eb keq t\u00eb Nash-it. \u00c7do spital donte q\u00eb t\u00eb t\u00ebrhiqte student\u00ebt m\u00eb t\u00eb mir\u00eb t\u00eb mjek\u00ebsis\u00eb, dhe meq\u00eb k\u00ebta ishin t\u00eb rrall\u00eb, shkaku i luft\u00ebs, spitalet fokusoheshin n\u00eb nj\u00eb gar\u00eb p\u00ebrmes s\u00eb cil\u00ebs ata shum\u00eb m\u00eb her\u00ebt d\u00ebrgonin oferta premtuese tek kandidat\u00ebt. \u00c7far\u00eb ishte m\u00eb e mira p\u00ebr nj\u00eb spital t\u00eb vet\u00ebm ishte e tmerrshme p\u00ebr kolektivin: spitalet detyroheshin t\u00eb pun\u00ebsonin student\u00eb p\u00ebrpara se ata t\u2019i kryenin provimet. Edhe student\u00ebt po ashtu e urrenin k\u00ebt\u00eb, por nuk kishin zgjidhje tjet\u00ebr marr\u00eb parasysh ofertat konkurruese.<\/p>\n

P\u00ebrkund\u00ebr letrave dhe rezolutat nga t\u00eb gjitha asociacionet mjek\u00ebsore, si dhe nga vet\u00eb student\u00ebt, problemi u zgjidh vet\u00ebm pas nj\u00eb dekade, dhe s\u00eb fundi me nj\u00eb dizajn n\u00eb vitet 1990-ta nga Elliot Peransond dhe Alvin Roth (i cili m\u00eb von\u00eb fitoi \u00e7mimin Nobel). Sot, student\u00ebt d\u00ebrgojn\u00eb preferencat e tyre dhe p\u00ebrcaktohen n\u00eb spitale duke u bazuar n\u00eb algoritmin q\u00eb siguron se \u00e7do student mund t\u00eb ndryshojn\u00eb preferencat e deklaruara dhe mund t\u00eb d\u00ebrgohen n\u00eb spitalet m\u00eb t\u00eb d\u00ebshirueshme, t\u00eb cilat do t\u00eb ishin t\u00eb lumtura t\u2019i pranonin ata, dhe asnj\u00eb spital nuk mund t\u00eb dal\u00eb jasht\u00eb sistemit dhe t\u00eb kap\u00eb pun\u00ebtor\u00eb m\u00eb t\u00eb mir\u00eb. Sistemi n\u00eb vete ka ekuilibrin e Nash-it: t\u00eb gjith\u00eb jan\u00eb duke b\u00ebr\u00eb m\u00eb t\u00eb mir\u00ebn q\u00eb munden duke u bazuar n\u00eb at\u00eb se \u00e7ka jan\u00eb duke b\u00ebr\u00eb t\u00eb tjer\u00ebt.<\/p>\n

Disa aplikime tjera politike p\u00ebrfshijn\u00eb ankandin e qeveris\u00eb britaneze p\u00ebr licencat e operimit t\u00eb 3G telekom dhe telefonave mobil n\u00eb vitin 2000. Mblodhi teoricient\u00ebt e loj\u00ebs q\u00eb t\u00eb ndihmojn\u00eb t\u00eb dizajnojn\u00eb ankandin duke p\u00ebrdorur disa implikime t\u00eb ekuilibrit t\u00eb Nash-it, dhe p\u00ebrfundoi duke p\u00ebrfituar 22.5 miliard\u00eb paund \u2013 edhe pse disa ishin t\u00eb pak\u00ebnaqur me rezultatet. Implikimet e Nash-it gjithashtu ndihmuan t\u00eb shpjegojn\u00eb se pse shtimi i nj\u00eb rruge n\u00eb rrjetin e transportit mund ta b\u00ebj\u00eb udh\u00ebtimin m\u00eb t\u00eb gjat\u00eb. Vozit\u00ebsit egoist\u00eb duke zgjedhur rrug\u00ebn m\u00eb t\u00eb shkurt\u00ebr nuk e llogarisin efektin e tyre q\u00eb ndikon n\u00eb rritjen e koh\u00ebzgjatjes s\u00eb udh\u00ebtimit t\u00eb tjetrit, dhe k\u00ebshtu mund t\u00eb prishin shkurtes\u00ebn e re. Nj\u00eb studim i publikuar n\u00eb vitin 2008 gjeti shtat\u00eb lidhje rrug\u00ebsh n\u00eb Lond\u00ebr dhe 12 n\u00eb New York ku mbyllja e tyre mund t\u00eb nxist\u00eb rrjedh\u00ebn e trafikut.<\/p>\n

Loja filloi<\/strong><\/p>\n

Ekuilibri i Nash-it nuk do t\u00eb arrinte suksesin q\u00eb kishte pasur pa disa p\u00ebrpunime n\u00eb iden\u00eb origjinale. S\u00eb pari, n\u00eb shum\u00eb prej situatave, ka m\u00eb shum\u00eb se nj\u00eb gjas\u00eb t\u00eb ekuilibrit t\u00eb Nash-it. Vozit\u00ebsit zgjedhin se n\u00eb cil\u00ebn an\u00eb t\u00eb rrug\u00ebs t\u00eb vozisin si reagim i sjelljes s\u00eb vozit\u00ebsit tjet\u00ebr \u2013 me rezultate shum\u00eb t\u00eb ndryshme, var\u00ebsisht se ku jeton; n\u00eb Britani vozitet n\u00eb an\u00ebn e majt\u00eb t\u00eb rrug\u00ebs, nd\u00ebrsa n\u00eb Amerik\u00eb n\u00eb an\u00ebn e djatht\u00eb. Zhg\u00ebnjim shtes\u00eb p\u00ebr ekonomist\u00ebt q\u00eb mbartin si arm\u00eb kryesore algjebr\u00ebn, t\u00eb kuptuarit e strategjis\u00eb k\u00ebrkon dije rreth normave sociale dhe zakoneve. Vet\u00ebm teorema e Nash-it nuk ishte e mjaftueshme.<\/p>\n

P\u00ebrpunimi i dyt\u00eb p\u00ebrfshiu marrjen n\u00eb llogari si\u00e7 duhet t\u00eb k\u00ebrc\u00ebnimeve jokredibile. N\u00eb qoft\u00eb se nj\u00eb tinejxher k\u00ebrc\u00ebnon t\u00eb ik\u00eb nga sht\u00ebpia, n\u00eb qoft\u00eb se n\u00ebna e tij ia largon telefonin mobil, at\u00ebher\u00eb \u00ebsht\u00eb ekuilibri i Nash-it kur ajo ia jep telefonin p\u00ebr t\u00eb arritur paqe t\u00eb mendjes. Por, Reinhard Selten, nj\u00eb ekonomist gjerman, i cili n\u00eb vitin 1944 s\u00eb bashku me Nash dhe John Harsanyi ndan\u00eb \u00e7mimin Nobel, argumentoi se ky nuk \u00ebsht\u00eb nj\u00eb rezultat bind\u00ebs. N\u00ebna duhet t\u00eb di se k\u00ebrc\u00ebnimi i f\u00ebmij\u00ebs s\u00eb saj \u00ebsht\u00eb i that\u00eb \u2013 pa marr\u00eb parasysh se sa tragjike \u00ebsht\u00eb humbja e telefonit, nj\u00eb nat\u00eb n\u00eb rrug\u00eb mund t\u00eb jet\u00eb m\u00eb e keqe. Ajo thjesht mund ta konfiskoj\u00eb telefonin, duke e detyruar djalin e saj t\u00eb fokusohet n\u00eb detyrat e sht\u00ebpis\u00eb.<\/p>\n

Puna e zotit Selten, la ekonomist\u00ebt t\u00eb gdhendin dhe t\u00eb gjenin gjasat e mundshme t\u00eb ekuilibrit t\u00eb Nash-it. Harsanyi adresoi faktin se n\u00eb shum\u00eb prej loj\u00ebrave t\u00eb jet\u00ebs reale, njer\u00ebzit jan\u00eb t\u00eb pasigurt se \u00e7far\u00eb do kund\u00ebrshtari i tij. Ekonomist\u00ebt do ta kishin shum\u00eb problem t\u00eb analizojn\u00eb strategjit\u00eb m\u00eb t\u00eb mira p\u00ebr dy t\u00eb dashuruar q\u00eb mundohen t\u00eb zgjedhin nj\u00eb lokacion t\u00eb pranuesh\u00ebm p\u00ebr t\u00eb dyja pal\u00ebt p\u00ebr nj\u00eb takim, duke mos pasur iden\u00eb se \u00e7ka p\u00eblqen tjetri. Duke vendosur besimet e t\u00eb dy personave n\u00eb loj\u00eb (p\u00ebr shembull t\u00eb dy mendojn\u00eb nj\u00ebjt\u00eb, se tjetri i do picat po aq sa e do sushi-n) Harsanyi i dha zgjidhje k\u00ebtij problemi. Nj\u00eb tjet\u00ebr problem filloi t\u00eb shfaqet. Fuqia e parashikimit t\u00eb ekuilibrit t\u00eb Nash-it mb\u00ebshtetet n\u00eb sjelljen racionale. Shpesh njer\u00ebzit nuk jan\u00eb aq racional\u00eb. N\u00eb eksperimentet e replikimit t\u00eb dilem\u00ebs s\u00eb t\u00eb burgosurit, vet\u00ebm gjysma e njer\u00ebzve zgjedhin t\u00eb flasin. P\u00ebr ekonomist\u00ebt t\u00eb cil\u00ebt kan\u00eb b\u00ebr\u00eb \u00e7mos p\u00ebr t\u00eb futur racionalitetin (Nash gjithashtu) n\u00eb modelet e tyre, kjo ishte problematike. Cila \u00ebsht\u00eb nevoja p\u00ebr vendosjen e stimujve t\u00eb mir\u00eb, n\u00eb qoft\u00eb se njer\u00ebzit nuk ndjekin interesin e tyre m\u00eb t\u00eb mir\u00eb?<\/p>\n

Nuk kishte humbur e gjitha. Eksperimenti gjithashtu tregoi se eksperienca i b\u00ebn lojtar\u00ebt m\u00eb t\u00eb men\u00e7ur; afro raund-it t\u00eb dhjet\u00eb rreth 10% e lojtar\u00ebve filluan t\u00eb refuzojn\u00eb t\u00eb flisnin. Kjo i m\u00ebsoi ekonomist\u00ebt t\u00eb jen\u00eb m\u00eb t\u00eb kujdessh\u00ebm n\u00eb aplikimin e ekuilibrit t\u00eb Nash-it. Me loj\u00ebra t\u00eb komplikuara, apo me ata t\u00eb cil\u00ebt nuk kan\u00eb shans t\u00eb m\u00ebsojn\u00eb prej gabimeve, implikimet e ekuilibrit t\u00eb Nash, mund t\u00eb mos punojn\u00eb.<\/p>\n

Megjithat\u00eb, ekuilibri i Nash-it ka nj\u00eb rol ky\u00e7 n\u00eb mikroekonomin\u00eb moderne. Nash vdiq n\u00eb nj\u00eb aksident me makin\u00eb n\u00eb vitin 2015; asokohe sh\u00ebndeti i tij mendor ishte p\u00ebrmir\u00ebsuar, ai kishte vazhduar\u00a0ligjerimin n\u00eb Princeton dhe e kishte marr\u00eb \u00e7mimim Nobel.<\/p>\n

_____<\/p>\n

Artikulli origjinal<\/a><\/p>\n

P\u00ebrktheu: Besnik Rexhepi<\/p>\n

 <\/p>\n<\/div>\n

\n
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\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"

Shkrimi i pest\u00eb nga idet\u00eb themelore t\u00eb ekonomis\u00eb zb\u00ebrthen ekuilibrin e Nash-it John Nash arriti n\u00eb Universitetin e Princeton n\u00eb vitin 1938 p\u00ebr t\u00eb filluar doktorat\u00ebn me let\u00ebr rekomandimi n\u00eb nj\u00eb fjali: \u201cAi \u00ebsht\u00eb nj\u00eb gjeni i matematik\u00ebs\u201d. Nuk zhg\u00ebnjeu. Vet\u00ebm 19 vje\u00e7ar dhe me p\u00ebrfundimin e vet\u00ebm nj\u00eb l\u00ebnd\u00eb t\u00eb ekonomis\u00eb gjat\u00eb universitetit, n\u00eb […]<\/p>","protected":false},"author":490,"featured_media":10459,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[1366,1880,1879],"ppma_author":[1311],"class_list":["post-4021","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","tag-ekonomia","tag-ekuilibri","tag-nash-i"],"authors":[{"term_id":1311,"user_id":490,"is_guest":0,"slug":"the-economist","display_name":"The Economist","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/291dfc1ba0656c52b0678303278a9c43f1d5025bd12da6c36aaec7dd5b5deea9?s=96&d=mm&r=g","user_url":"","last_name":"Economist","first_name":"The","description":""}],"_links":{"self":[{"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/posts\/4021","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/users\/490"}],"replies":[{"embeddable":true,"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/comments?post=4021"}],"version-history":[{"count":3,"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/posts\/4021\/revisions"}],"predecessor-version":[{"id":10460,"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/posts\/4021\/revisions\/10460"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/media\/10459"}],"wp:attachment":[{"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/media?parent=4021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/categories?post=4021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/tags?post=4021"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/sbunker.org\/en\/wp-json\/wp\/v2\/ppma_author?post=4021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}