Koh Jin Ming, Cheong Kang Hao
Science, Mathematics and Technology Cluster Singapore University of Technology and Design (SUTD) 8 Somapah Rd Singapore S487372 Singapore.
California Institute of Technology Pasadena CA 91125 USA.
Adv Sci (Weinh). 2020 Nov 7;7(24):2001126. doi: 10.1002/advs.202001126. eCollection 2020 Dec.
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.
在博弈论中，帕隆多悖论描述了通过在失败策略之间交替从而实现获胜结果的可能性。该框架最初是从一种被称为闪烁布朗棘轮的物理现象中概念化而来的，但此后在理解物理和生命科学中的广泛现象方面很有用，包括生态系统的行为和进化趋势。该悖论的一个最简表示是一对按随机顺序进行的游戏；不幸的是，在所有参数中通用的闭式解仍然难以捉摸。在这里，我们给出了广义游戏对的资本统计和结果条件的显式解。该方法具有通用性，可应用于棘轮型模型以及一般的帕隆多悖论的分析方法的开发，这些模型和悖论在物理和生物系统中有广泛应用。
