MARKOV O'YINLARI VA ULARNI BELLMAN-SHAPLEY TENGLAMASI YORDAMIDA YECHISH
Keywords:
Kalit so'zlar: Markov o'yinlari, stoxastik o'yin, Shapley teoremasi, Bellman- Shapley tenglamasi, Nash muvozanati, qiymat funksiyasi, qiymat iteratsiyasi, diskontlangan mukofot, optimal siyosat, minimaks qiymat.Abstract
Annotatsiya. Ushbu maqolada jarayonlar tadqiqoti va optimal boshqaruvning
muhim yo'nalishlaridan biri — Markov o'yinlari (stoxastik o'yinlar) tahlil qilinadi.
Maqolada Lloyd Shapley tomonidan 1953-yilda kiritilgan Markov o'yinining
matematik shakllanishi, asosiy turlari (nol yig'indili, umumiy yig'indili, kooperativ va
kooperatsiz, chekli va cheksiz gorizontli, diskontlangan va o'rtacha mukofotli) hamda
yechim kontseptsiyalari ko'rib chiqiladi. Nazariy tahlil natijalari amaliy holat asosida
— ikki firma o'rtasidagi reklama strategiyasi raqobati misolida — Bellman-Shapley
rekurrent tenglamasi yordamida qadam-baqadam yechiladi. Qiymat iteratsiyasi
algoritmi orqali har bir holat uchun optimal qiymat funksiyasi va muvozanat siyosati
topiladi.
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