One Dimensional Asynchronous Cooperative Parrondo's Games

TL;DR

This paper presents an analytical approach and algorithm for understanding the probability distribution in one-dimensional asynchronous cooperative Parrondo's games, highlighting how the paradox depends on the number of players.

Contribution

It introduces a new analytical method and algorithm for the probability distribution in cooperative Parrondo's games, emphasizing the role of player count.

Findings

Winning depends on the number of players

Analytical results match simulations

Paradox occurrence varies with player number

Abstract

An analytical result and an algorithm are derived for the probability distribution of the one-dimensional cooperative Parrondo's games. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.