THE k-PROPORTIONAL τ-VALUE: EXTENDING COOPERATIVE SOLUTIONS IN BIG BOSS GAMES
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, cilt.21, ss.7246-7257, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 21
- Basım Tarihi: 2025
- Doi Numarası: 10.3934/jimo.2025168
- Dergi Adı: JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Compendex, MathSciNet, zbMATH
- Sayfa Sayıları: ss.7246-7257
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
. In this study, we introduce the k-proportional tau-value, a novel generalization of the tau-value for cooperative games, achieved by modifying the minimal right vector with a proportionality factor, k. We derive this solution concept specifically for big boss games, where a dominant player significantly influences coalition outcomes while others depend on their participation. The k-proportional tau-value is shown to consistently produce core allocations in big boss games, with the parameter k enabling flexible adjustments to payoff distributions. We apply this framework to a real-world case study, modeling Amazon's internal collaboration for an AI-driven personalized shopping recommendation system, using data from Amazon's annual report to estimate coalition values and compute payoff distributions. This approach provides a robust tool for analyzing cooperative settings with hierarchical structures, applicable to contexts such as production, management, inventory, warehousing, storage, and information markets.