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

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  • Song-Ju Kim
  • Taiki Takahashi
  • Kazuo Sano

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.

Suggested Citation

  • Song-Ju Kim & Taiki Takahashi & Kazuo Sano, 2021. "A Balance for Fairness: Fair Distribution Utilising Physics in Games of Characteristic Function Form," Papers 2101.11496, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:2101.11496
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    References listed on IDEAS

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    1. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Robert J. Aumann, 2025. "Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 9, pages 219-242, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

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