石头-纸-剪刀游戏的复制器-变异器动态:通过错误来学习
Suman Chakraborty1, Ishita Agarwal1, Sagar Chakraborty1
1Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India.
Physical review. E
|April 18, 2024
概括
学习模型中的错误可以令人惊地改善玩家的策略,甚至可以导致像石纸剪刀这样的游戏中的理性纳什平衡结果. 这项研究为复制者-突变者方程引入了一个新的哈密尔顿结构.
科学领域:
- 进化游戏理论 进化游戏理论
- 数学生物学 数学生物学
- 复杂系统动力学 复杂系统动力学
背景情况:
- 布什-莫斯泰勒,罗斯-埃雷夫和社会学习模型的概括对于理解战略演变至关重要.
- 将错误 (突变) 纳入学习模型对于现实的模拟至关重要.
- 石头-纸-剪刀游戏是研究周期动态和战略相互作用的基本模型.
研究的目的:
- 将现有的学习模型概括为包含错误,从而导致复制者-突变者方程.
- 在各种突变模式下分析石头-纸-剪刀游戏的动态.
- 调查错误对学习,战略融合和混乱行为的影响.
主要方法:
- 布什-莫斯泰勒,罗斯-埃雷夫和社会学习模型的泛化,包括附加性或乘法性突变.
- 非对称分析来导出非线性复制者-突变者方程.
- 详尽调查岩石-纸-剪刀游戏的分析可处理的突变模式.
- 游戏动态的分析,包括极限周期和混乱轨道.
主要成果:
- 复制器-突变器方程具有增增或乘数突变,它是从一般化的学习模型中产生的.
- 丰富的动态,包括极限周期和混乱的轨道,在岩石纸剪刀游戏中观察到.
- 错误可以促进学习,并引导玩家在对称和不对称的游戏中获得合理的纳什平衡结果.
- 确定了一个新的哈密尔顿结构用于复制者-突变者方程.
结论:
- 错误,通常被认为是有害的,可以在进化学习和战略优化中发挥建设性的作用.
- 将突变纳入学习模型可以稳定复杂的系统,并导致可预测的,合理的结果.
- 发现的哈密尔顿结构为进化动态的理论分析提供了新的途径.
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