Boltzmann和Fokker-Planck方程模拟具有学习效应的Elo评级系统
Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects
摘要：
在本文中，我们提出并研究了一个新的动态评级模型的大量球员，这是著名的Elo评级系统的动机。每个玩家都有一个内在的实力和一个评级，这两个都是在每场比赛后更新。我们的状态和分析相应的玻尔兹曼型方程，并推导出相应的非线性，非局域福克-普朗克方程。本文研究了Fokker-Planck方程解的存在性，并讨论了它们在长时间极限下的行为。此外，我们说明了玻尔兹曼和福克-普朗克方程的动力学与各种数值实验。
英文摘要：
In this paper we propose and study a new kinetic rating model for a large number of players, which is motivated by the well-known Elo rating system. Each player is characterised by an intrinsic strength and a rating, which are both updated after each game. We state and analyse the respective Boltzmann type equation and derive the corresponding nonlinear, nonlocal Fokker-Planck equation. We investigate the existence of solutions to the Fokker-Planck equation and discuss their behaviour in the long time limit. Furthermore, we illustrate the dynamics of the Boltzmann and Fokker-Planck equation with various numerical experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
