Nash ma'auni. A ka'idar wasanni for tattalin arziki (Dzhon Nesh)

A cikin 1930s, Dzhon Fon Neyman da Oskar Morgenstern ya zama cikin wadanda suka kafa sabuwar ban sha'awa yankunan lissafi, wanda aka kira "Game Theory." A cikin 1950s wannan Trend zama sha'awar a cikin matasa lissafi Dzhon Nesh. ma'auni ka'idar ya zama batun da ya sabawa rubuce-rubucensu, wanda ya rubuta a cikin shekaru 21 da haihuwa. Kamar wancan ne aka haifi wani sabon dabarun game kira "Nash ma'auni", cancanci kyautar Nobel shekaru masu yawa daga baya - a shekarar 1994.

The dogon rata tsakanin rubuce-rubuce na dissertation, kuma ya kasance mai karbuwa a duniya gwajin for lissafi. Genius ba tare da sanin sa a tsanani shafi tunanin mutum cuta, amma kuma da aiki Dzhon Nesh ya iya shirya godiya ga kyau kwarai logicheskumu hankali. Ka'idarsa na "Nash ma'auni" aka bayar da Nobel Prize, da kuma rayuwarsa a cikin fim karbuwa daga «Beautiful hankali» ( «A Beautiful Zuciya") film.

A takaice a wasan ka'idar

Tun da ka'idar Nash ma'auni ya bayyana adam hali cikin sharuddan hulda, don haka ya kamata ka yi la'akari da asali Concepts na wasan ka'idar.

Game ka'idar karatu da hali na mahalarta (jamiái) a cikin yanayi na hulda da juna a kan irin wasan a cikin abin da sakamako dogara a kan yanke shawara da kuma hali na 'yan mutane. Jam'iyyar za dauki yanke shawara bisa tsammanin su game da hali na wasu, da kuma cewa da aka kira wata caca da dabarun.

Akwai kuma rinjaye dabarun, a cikin abin da yar sami sakamako mafi kyau ga kowane hali na sauran mahalarta taron. Wannan shi ne mafi kyau dabarun bezproigryshnaya player.

Fursuna ta rudanin da nasara

fursuna rudanin - shi ne yanayin da wasan, inda 'yan wasa suna tilasta su yin m yanke shawara, da cimma manufa daya a rikicin zabi. The tambaya ne, wanda daga cikin wadannan zažužžukan shi nã zãɓen, farga sirri da kuma janar sha'awa, kazalika da rashin samun wani abu, kuma mafi. 'Yan wasa kamar kewaye a cikin wani m Playing yanayi, wanda wani lokacin da ke sa su tunanin sosai m.

Wannan takaddamar da bincika Amirka lissafi Dzhon Nesh. Ma'auni, wanda ya jagoranci, ya sauyi a yadda hanya. A karfi sabon tunani rinjayi ra'ayi na tattalin arziki game da yadda za a yi wani iri-iri na 'yan wasa a kasuwa, shan la'akari da bukatun wasu, tare da m hulda da kuma rarrabawa da bukatun.

Shi ne mafi kyau don nazarin wasan ka'idar da kankare misalai, domin wannan sosai ilmin lissafi horo ba a bushe da msar tambayar.

Wani misali da wani fursuna ta rudanin

Misali Biyu mutane yi fashi, fada a hannun 'yan sanda da ake yi masa tambayoyi, a raba bẽnãye. A daidai wannan lokaci da 'yan sanda da ministoci bayar da kowane ɗan takara sharadi gwargwado a karkashin abin da za a saki a cikin hali da shaida a da abokin tarayya. A kowane daga cikin masu laifin nan gaba kafa na dabarun da zai la'akari da:

1. Duka a lokaci guda zuwa ga shaida, kuma samun a kurkuku 2.5 years.
2. Duka a lokaci guda shiru kuma sami shekara 1, domin a cikin wannan harka da shaida tushe na su da laifi zai kasance kananan.
3. Daya yana ba da shaida da kuma samu cikin 'yanci, da kuma sauran ne shiru da kuma samun 5 shekaru a gidan yari.

Babu shakka, da sakamako daga cikin akwati ya dogara da shawarar da jam'iyyun biyu, amma ba za su iya zo da wani yarjejeniya, domin yana zaune a daban-daban Kwayoyin. Har ila yau, a fili a bayyane rikici na sirri sha'awa da yaki ga gayya. Kowace daga cikin fursunonin da biyu zažužžukan, da kuma 4 daban-daban sakamakon.

Circuit ma'ana inferences

Saboda haka, laifin amma don la'akari da zaɓuɓɓuka masu biyowa:

1. Ina shiru da kuma shiru na abokin - mu duka biyu samu 1 shekara a kurkuku.
2. Na hayan abokin tarayya, kuma ya hannãye da ni - mu duka biyu samu 2.5 years a kurkuku.
3. Ni shiru, da kuma abokin tarayya ba up - Zan samu shekaru 5 a gidan yari, kuma shĩ ne free.
4. Na hayan fitar da wani abokin tarayya, amma ya ne shiru - I samun 'yanci, kuma ya 5 shekaru a gidan yari.

Ga wani matrix na yiwuwa mafita da kuma sakamakon ga tsabta.

Table m sakamakon fursuna ta rudanin.

A tambaya shi ne cewa kowane ɗan takara zai zabi?

"Yi shiru, ba za ka iya ce" ko "ba zai iya ci gaba da shiru, to magana"

Don gane da jam'iyyar ta zabi, kana bukatar ka je ta hanyar da sarkar daga cikin tunani. Wadannan da tattaunawa da laifi Kuma idan na ce kome da kome ce abokin tarayya, za mu samu wani m lokaci (1 shekara), amma ina ba zai iya ganin yadda zai tafiyar da rayuwarsu. Idan ya bada shaida gāba da ni, ina ma mafi alhẽri ga bayar da shaida, ko zan iya zauna don 5 shekaru. Ban so zama a kan 2.5 shekaru fiye da 5 shekaru. Idan zai ce kome ba, zan musamman bukatar shaida, saboda ina samun haka free. Hakazalika, tattaunawa da kuma jam'iyyar B.

Abu ne mai sauki mu fahimci cewa rinjaye dabarun domin kowane daga cikin masu laifin - shi ne bãyar da shaida. A ganiya batu na wannan wasan ya auku a lokacin da biyu da laifin shaida, kuma su sami "kyauta" - 2.5 years a kurkuku. Nash ta ka'idar wasanni kira shi balance.

Suboptimal Nash mafi kyau duka bayani

Revolutionariness neshevskogo duba da cewa irin wannan ma'auni ne ba mafi kyau duka, idan muka yi la'akari da mutum yar da sirri sha'awa. Bayan duk, mafi wani zaɓi - shi ne su yi shiru da za a sake.

Nash ma'auni - shi ne batu na lamba ban sha'awa, a cikinsa kowaccen ance wannan zabin da cewa mafi kyau ga shi kawai bayar da cewa sauran mahalarta zabi wani musamman da dabarun.

Idan akai la'akari da embodiment, a lokacin da biyu da laifin shiru kuma sami kawai zuwa shekara 1, zai iya yiwuwa a kira Pareto mafi kyau duka bambanci. Duk da haka, shi ne kawai zai yiwu dã mãsu laifi sun iya zo wata yarjejeniya a gaba. Amma ko da wannan zai ba da tabbacin wannan sakamako, domin da jaraba ja da baya daga fatauci da kuma kauce wa azãba mai girma. Rashin cikakkiyar amincewa a juna da hatsarin don samun 5 shekaru tilasta ka zaɓi tare da fitarwa. Don yin tunãni a kan gaskiyar cewa mahalarta za su tsaya ga version tare da shiru, mukaddashin a shagali, kawai m. Irin wannan ƙarshe za a iya sanya, idan muka yi nazarin Nash ma'auni. Misalai kawai tabbatar da dama.

M ko tunanin mutuntaka

ma'auni ka'idar Nash ba mai ban mamaki karshe oprovergnuvshie data kasance kafin ka'idojin. Alal misali, Adam Smith dauke da hali na kowane daga cikin mahalarta a matsayin gaba daya m, kuma Yanã fitar da tsarin da baya cikin balance. Wannan ka'idar da aka kira da "ganuwa hannun kasuwar".

Dzhon Nesh ga cewa idan dukan jam'iyyun za su yi aiki, bi kawai da bukatunta, shi ba zai kai ga ganiya kungiyar sakamakon. Ganin cewa m tunani ne muhimmi ga kowane ɗan takara, mafi kusantar zabi, wanda yayi dabarun Nash ma'auni.

Zalla namiji gwaji

A daukan hankali misali ne game "m paradox", wanda, ko da yake alama daga wurin, amma shi ne mai m hoto cewa ya nuna yadda ka'idar Nash wasanni.

A cikin wannan wasan kana bukatar su yi tunanin cewa kamfanin free maza zo a cikin mashaya. Kusa ne kamfanin na 'yan mata, daya daga wanda ke fin so ga wasu, sai ka ce da m. Kamar yadda boys su dõra, don samun mafi kyau budurwa da kanka?

Saboda haka mutane tattaunawa: idan kowa da kowa zai sami Mai ƙididdigewa ga m, sa'an nan mafi m, shi ba zai samu kowa, sa'an nan ta abokai ba zai so ya son. Babu wanda yake so ya zama na biyu fall-baya zaɓi. Amma idan ka mutane zabi su kauce wa m, sa'an nan da yiwuwar kowane daga cikin mutane a sami mai kyau aboki tsakanin 'yan mata ne high.

Nash ma'auni halin da ake ciki shi ne ba da mafi kyau duka ga mutane, saboda, bi kawai nasu son zuciyarsu, wanda zai zaɓi wani m. Yana da aka gani cewa kawai bin son zuciyarsu zai zama suna tantamar zuwa auka daga cikin kungiyar amfane shi. Nash ma'auni zai nufin cewa kowane Guy yana aiki a kansa bukatun, abin da suke a lamba tare da bukatun da dukan kungiyar. Wannan sub-mafi kyau duka zaɓi don kowane mutum, amma mafi kyau duka domin kowane, dangane da jimlar nasarar da dabarun.

Our dukan rai ne a wasan

Yanke shawara a cikin real duniya ne sosai kama da wasan, inda za ka sa ran wani m hali daga sauran members. A kasuwanci, yin aiki a cikin tawagar, a cikin kamfanin, ko ma cikin dangantaka tare da akasin jima'i. Daga manyan ma'amaloli da kuma talakawa rayuwa yanayi duk abin da yake ƙarƙashin wani musamman doka.

Hakika, wasan yanayi dauke laifi da kuma bar - yana da kyau kwarai kawai misalai da nuna wani Nash ma'auni. Misalai na irin wannan dilemmas sau da yawa bayyana a cikin real kasuwar, da kuma musamman a cikin hali na biyu monopolies iko kasuwa.

gauraye da dabarun

Sau da yawa mun vovlekaemy ba a daya amma a wasanni da yawa. By zabar daya daga cikin zabin da wannan wasan, shiryar da mai m dabarun, amma samun wani daban-daban game. Bayan da dama m yanke shawara, za ka ga cewa your sakamakon ba. Abin da ya dauki?

La'akari iri biyu dabarun:

• Pure dabarun - ne da hali na takara, wanda dogara ne a kan tunani a kan zai yiwu hali na sauran mahalarta taron.
• Mixed dabarun ko m dabarun - wannan canzawar m dabarun bazuwar selection ko m dabarun da wasu yiwuwa. Wannan dabarar kuma ake kira rendomizirovannoy.

Ganin wannan hali, za mu samu wani sabon hangen zaman kan ma'auni na Nashua. Idan a baya cewa dan wasan na zaban dabarun da zarar yana yiwuwa su yi tunanin, da kuma sauran hali. Yana iya zaci cewa zaɓi cewa 'yan wasa zabi dabarun da ka tare da wasu yiwuwa. Wasanni a cikin abin da ba za ka iya samun Nash ma'auni a cikin m dabaru, ko da yaushe sun su gauraye.

Nash ma'auni a gauraye dabarun kira gauraye ma'auni. Yana da wani balance, inda kowane ɗan takara na zaban ganiya mita zabi su da dabarun, bayar da cewa wasu mambobin zabi su da dabarun da wani qaddara mita.

Hukunci da kuma gauraye dabarun

Wani misali da wani gauraye dabarun za a iya sa a wasan na kwallon kafa. A mafi kyau hoto na gauraye dabarun - wannan shi ne mai yiwuwa a jerin bugun fanareti. Saboda haka, muna da golan wanda zai iya tsalle kawai a daya kusurwa, da kuma wasan wanda ke faruwa a duka da wata azãba.

Saboda haka, idan karo na farko da wani dan wasa ya so da wani dabarun yin wani tasiri a hagu kusurwa da kuma mai tsaron gida ma fada cikin wannan kusurwa kuma kama da ball, yadda events zai iya ci gaba a karo na biyu? Idan wani player da yake faruwa a doke da m kusurwa, shi ne iya zama ma a bayyane yake, amma kuma a buga a wannan kwana babu kasa a bayyane yake. Saboda haka, Goalkeeper, da kuma batter yana da wani zabi, amma su dõgara a kan bazuwar selection.

Saboda haka, alternating bazuwar selection na wani m dabarun, player da golan pytajutsja don samun matsakaicin sakamako.