Generalized Solutions of Parrondo's Games,Advanced Science

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Generalized Solutions of Parrondo's Games
Advanced Science ( IF 14.3 ) Pub Date : 2020-11-07 , DOI: 10.1002/advs.202001126
Jin Ming Koh _{1,

2} , Kang Hao Cheong _{1,

3}

Affiliation

In game theory, Parrondo's paradox describes the possibility of achieving winning outcomes by alternating between losing strategies. The framework had been conceptualized from a physical phenomenon termed flashing Brownian ratchets, but has since been useful in understanding a broad range of phenomena in the physical and life sciences, including the behavior of ecological systems and evolutionary trends. A minimal representation of the paradox is that of a pair of games played in random order; unfortunately, closed‐form solutions general in all parameters remain elusive. Here, we present explicit solutions for capital statistics and outcome conditions for a generalized game pair. The methodology is general and can be applied to the development of analytical methods across ratchet‐type models, and of Parrondo's paradox in general, which have wide‐ranging applications across physical and biological systems.

中文翻译：

帕隆多游戏的广义解

在博弈论中，帕隆多悖论描述了通过交替失败策略来实现获胜结果的可能性。该框架是从一种称为闪烁布朗棘轮的物理现象概念化的，但此后一直有助于理解物理和生命科学中的广泛现象，包括生态系统的行为和进化趋势。该悖论的最简表现是一对以随机顺序进行的游戏。不幸的是，所有参数通用的封闭式解决方案仍然难以捉摸。在这里，我们提出了广义博弈对的资本统计和结果条件的明确解决方案。该方法是通用的，可应用于棘轮型模型分析方法的开发，以及一般帕隆多悖论的分析方法，这些方法在物理和生物系统中具有广泛的应用。

更新日期：2020-12-16

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