Noise in Parrondo's paradox: periodic variation in cooperative Parrondo games

Abstract

Parrondo's paradox is becoming increasingly relevant in the natural sciences and biology since it is used as a paradigm in various ecological scenarios. Periodic fluctuations were incorporated into a Capital-dependent Parrondo's model in a recent study because periodic and quasi-periodic events are frequently seen not only in nature but also in areas of economics. However, a more comprehensive model is necessary due to the prevalence of biological and social systems characterized by Cooperative and Capital-dependence. We first extend the Cooperative variant of Parrondo's paradox to incorporate periodicity, followed by a switching strategy to show the existence of the Parrondo Effect. By incorporating both capital and cooperation, a new, unified model of Parrondo's Games can be developed for extensive application in ecological and economic contexts, such as behavioral diversity and noise in the stock markets.