Nazariyai boziho

Nazariyai boziho, yak fasli matematikaro guyand, ki dar vaziyati ikhtilof (yane dar surati ba ham zid omadann manfiati du va yo chand tarafho) qoidahoi ba dast ovardani natijahoi behtarinro me­omuzad. Khususiyati vaziyathoi ikhtilofi on ast, ki tarafho amaliyoti harifi khudro peshaki namedo­nand. Az hamin sabab Nazariyai bozihoro chun nazariyai qabul namudann qarorho dar vaziyathoi nomuayyan muoina mekunand.

Baroi on ki tahlili qonuniyathoi miqdorii vaziyathoi ikhtilofi im- konnazir gardad, modeli soddai on tartib doda meshavad, ki bozi nom dorad. Bozi bo qoidahoi shartie, ki amalhoi imkonpaziri tarafhoro ifoda mekunad va natijai bozi, ki bo majmui amalho ba dast meoyad, muayyan karda meshavad. Misoli boziho: shohmot, shashka, qarta. Agar dar bozi du harif ishtirok kunad, bozi dukasa va agar shumorai harif on az in ziyod boshad, bozi bisyor- kasa nomida meshavad. Natijai bozi bo burdi tarafho muayyan karda me­shavad. Bozie, ki dar on hosili jami hamai burdho barobari sifr ast, bozii hosili jamash sifri nom dorad. Dar bozihoi dukasai ho­sili jamashon sifri manfiati ta­rafho ba hamdigar tamoman muqobiland. In navi odditarini boziho beshtar tadqiq karda shudaand. Yake az mafhumhoi asosii Nazariyai boziho stra­tegiya (majmui qoidahoe, ki vobasta ba rafti bozi intikhob kardani in  yo on amalro yakqimmata muayyan me­kunad) meboshad. Vazifai bozi az tarafi bozingar intikhob karda shudani chunin strategiyaest, ki burdi kalontarin orad. Burde, ki yake az bozingaron hangomi az tarafi harifon istifoda shudani strategiyahoi intikhob kardaashon ba dast meorad, arzishi bozi nom dorad. Agar har yak bozingar faqat shumorai muayyani strategiya doshta boshad, bozi b o i n t i h o, dar mavridi baraks beiitiho nomida meshavad. Bo­zii dukasai bointiho hangomi m strategiya doshtani bozingari yakum va p strategiya doshtani bozingari duyum bozii tkhp yo bozii matrisagi nom dorad. Dar in holat boziro tavassuti matrisai rosshkunja muayyan kardan mumkin ast, ki satrhoi on ba strategiyahoi yak bozingar, sutunhoyash ba strategiyahoi bozingari du­yum muvofiqat mekunad, elementhoi matrisa boshad, burdi boziigari yakumro hangomi az strategiyahoi muvofiq istifoda burdani harifon ifoda mekunad. Natijahoi asosii Nazariyai bozi dar asosi prinsipi minimaks (kushini bozingar, ki dar sharoiti noqulaytarin rohi kutohi burdro mejuyad) ba dast omadaand; in prin­sip intikhobi strategiyaero tavsiya medihad, ki hangomi miqdori kamtarii amalhoi musoidi harif burdi beshtarinro tamin mekunad. Bozihoi matrisagii hosili jamashon sifri bo usulhoi programmonidani khatti va usulhoi iteratsiya hal kar­da meshavand. Baroi bozihoi beintiho, bozihoi bisyorkasa va bozihoi hosili jamashon gayrisifri hanuz usulhoi umumii hal yofta nashudaand. Bozihoi pozitsioni va differensiali niz tadqiq shuda istodaand.

Asosi Nazariyai boziro prinsipi minimaks, ki soli 1928 matematiki amerikoi Neyman tadjik namudaast, inchunnn tadqiqothoi matematikhoi nemis E. Sermelo va matematiki fransavi E. Borel ba vujud ovardaad. Badi chop shudani risolai J. Neyman va O. Morgenshterp «Nazariyai boziho va maromi iqtisod»  Nazariyai bozi ba sohai mustaqili matematika tabdil yoft.

Ad.: Vorobev N. N., Matematiche­skaya teoriya igr., L., 1963; Ventsel B. S., Elementi teorii igr., M., 1061; Neyman Dj., Morgenshtern O., Teoriya igr i ekonomicheskoe povedenie, per. s angl., M., 1970; Vorobev N. N., Teoriya igr (Leksii ekonomistov- kibernetikov), L., 1974.