A Balance for Fairness: Fair Distribution Utilising Physics in Games of Characteristic Function Form

TL;DR

This paper introduces a physics-inspired method to efficiently compute fair profit distributions in cooperative games, reducing computational complexity and enabling real-time adjustments.

Contribution

It proposes a novel physics-based approach to solve the nucleolus calculation problem in characteristic function games, improving efficiency and adaptability.

Findings

Significantly reduces computational complexity for nucleolus calculation.

Enables real-time response to parameter changes.

Demonstrates effectiveness through theoretical and experimental validation.

Abstract

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.