在本篇的論文中，我們探究艾爾法酒吧賽局(El Farol bar game)的折扣強化學習過程(discounted reinforcement learning process) ，並分析它。我們對這樣的強化學習過程推導出一個非線性微分方程組的系統，並從非線性系統(nonlinear system)中找出一些對應於賽局的奈許平衡(Nash equilibria of the game) 的平衡點。在這些穩
定的平衡點中，只有對應於純奈許平衡(pure Nash equilibria) 的平衡點是穩定的。其它對應於混合奈許平衡(mixed Nash equilibria)的平衡點則都是不穩定的。

In this paper we consider the discounted reinforcement learning process
of an El Farol bar game. We analyze a discounted reinforcement learning process of the El Farol Bar game. We derive a system of nonlinear differential equations for this process. We show that some equilibrium
points of this nonlinear system correspond to the Nash equilibria of the game. Among these stable equilibrium points only the equilibrium point that corresponds to pure Nash equilibrium is stable. Other equilibrium points that correspond to mixed Nash equilibria are unstable.

中文摘要
Abstract
Acknowledgements
List of Figures
List of Tables
1 Introduction------------------------------------1
2 Discounted Reinforcement Learning---------------4
2.0.1 Equilibrium points-----------------------8
2.0.2 Nash Equilibria-------------------------10
2.0.3 Stability-------------------------------13
3 Numerical Results------------------------------24
4 Conclusions------------------------------------27
Bibliography--------------------------------------28

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