A Balance for Fairness: Fair Distribution Utilising Physics in Games of Characteristic Function Form
This work addresses fairness in cooperative game theory, offering an incremental improvement for computational efficiency in distribution problems.
The authors tackled the problem of fair profit distribution in cooperative games by proposing a physics-inspired method that reduces computational complexity for calculating the nucleolus, achieving significant efficiency gains.
In chaotic modern society, there is an increasing demand for the realization of true 'fairness'. In Greek mythology, Themis, the 'goddess of justice', has a sword in her right hand to protect society from vices, and a 'balance of judgment' in her left hand that measures good and evil. In this study, we propose a fair distribution method 'utilising physics' for the profit in games of characteristic function form. Specifically, we show that the linear programming problem for calculating 'nucleolus' can be efficiently solved by considering it as a physical system in which gravity works. In addition to being able to significantly reduce computational complexity thereby, we believe that this system could have flexibility necessary to respond to real-time changes in the parameter.