停止器与单个控制器游戏与退化的扩散
Andrea Bovo1, Tiziano De Angelis1,2, Jan Palczewski3
1School of Management and Economics, Dept. ESOMAS, University of Torino, Corso Unione Sovietica 218 Bis, Torino, 10134 Italy.
Applied mathematics and optimization
|December 9, 2024
概括
这项研究涉及退化的随机游戏,证明游戏价值存在,并找到最佳的停止策略. 一种概率性扰动方法克服了退化扩散过程的分析局限性.
科学领域:
- 随机分析 随机分析
- 游戏理论 游戏理论
- 最佳控制控制的最佳方式
背景情况:
- 研究了具有退化的扩散动态的零和随机游戏.
- 由于退化的动态,标准分析方法是不够的.
研究的目的:
- 对于退化的随机游戏来说,确定游戏值的存在.
- 在这样的游戏中确定阻塞的最佳策略.
主要方法:
- 采用一种使用扩散扰动的概率方法.
- 分析了近似的非退化游戏的趋同.
- 为扰乱游戏构建最佳停止时间.
主要成果:
- 证明了退化的随机游戏存在游戏值的存在.
- 确定一个最佳的策略,用于堵塞.
- 显示扰乱游戏值和停止时间的收.
结论:
- 概率扰动方法成功地解决了退化的随机游戏.
- 原始游戏的最佳停止时间来自扰乱的解决方案.
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