Shapley value with coalition structures

• Main Author: Chan, Zi Hao
• Other Authors: PUN Chi Seng
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2021
• Subjects: Science::Mathematics::Applied mathematics::Game theory
• Online Access: https://hdl.handle.net/10356/148524
• Institution: Nanyang Technological University

Cooperative game theory aims to predict the formation of coalitions, analyze the joint actions taken by groups and evaluate the resulting collective payoffs. Shapley Value has been proven and widely used in many fields for its efficient, just and fair distribution of the collective payoffs to the players in the cooperative game. As an extension of Shapley Value, Owen Value was created to perform the fair payoff distribution for cooperative games having a division of players into unions. However, there are real-life cooperations that have further divisions amongst the division of players which are beyond the scope of what the existing Shapley and Owen Value formulas could calculate for. This necessitates a generalised value, which we call the Extended Value, to perform the payoff distribution in cooperative games having an arbitrary iterations of divisions amongst its players. Through the use of the tree data structure to extend Owen Value, the Extended Value is formed and is used on an example modelled after a COVID-19 vaccine R\&D cost sharing through international cooperation to illustrate the new value's applicability.