THE k-PROPORTIONAL τ-VALUE: EXTENDING COOPERATIVE SOLUTIONS IN BIG BOSS GAMES

Date

2025-10-25

Author

Ozcan, Ismail
Weber, Gerhard Wilhelm

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

75
views

0
downloads

Cite This

. 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.

URI

https://hdl.handle.net/11511/117094

Collections

Graduate School of Applied Mathematics, Article