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

arXiv: https://arxiv.org/abs/2101.11496 · HTML: https://mlsanity.com/paper/2101.11496/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 27 Jan 2021.

## Builds on (most cited first, 4 of 4)

- [The AI Economist: Improving Equality and Productivity with AI-Driven Tax Policies](https://mlsanity.com/paper/2004.13332/) (2020)
- [Ultrafast photonic reinforcement learning based on laser chaos](https://mlsanity.com/paper/1704.04379/) (2017)
- [Efficient Decision-Making by Volume-Conserving Physical Object](https://mlsanity.com/paper/1412.6141/) (2014)
- [Decision Maker based on Atomic Switches](https://mlsanity.com/paper/1507.05895/) (2015)

## Built on by (most cited first, 2 of 2)

- [Contextual Probability and Operational Minimality in Tug-of-War Decision Making](https://mlsanity.com/paper/2601.10034/) (2026)
- [Resource allocation method using tug-of-war-based synchronization](https://mlsanity.com/paper/2108.11979/) (2021)

## Abstract (arXiv)

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.