Steady states of an Elo-type rating model for players of varying strength

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2022-04-21 DOI:10.3934/krm.2023020

Bertram During, J. Evans, Marie-Therese Wolfram

引用次数: 0

Abstract

In this paper we study the long-time behaviour of a kinetic formulation of an Elo-type rating model for a large number of interacting players with variable strength. The model results in a non-linear mean-field Fokker-Planck equation and we show the existence of steady states via a Schauder fixed point argument. Our proof relies on the study of a related linear equation using hypocoercivity techniques.

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对于不同强度的玩家，elo型评级模型的稳定状态

在本文中，我们研究了具有可变强度的大量相互作用参与者的elo型评级模型的动力学公式的长期行为。该模型得到一个非线性平均场Fokker-Planck方程，并通过Schauder不动点论证证明了稳态的存在性。我们的证明依赖于使用低矫顽力技术研究一个相关的线性方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.