Parrondo games with spatial dependence, III

Abstract

We study Toral's Parrondo games with $N$ players and one-dimensional spatial dependence as modified by Xie et al. Specifically, we use computer graphics to sketch the Parrondo and anti-Parrondo regions for $3\le N\le 9$. Our work was motivated by a recent paper of Li et al., who applied a state space reduction method to this model, reducing the number of states from $2^N$ to $N+1$. We show that their reduced Markov chains are inconsistent with the model of Xie et al.

20 pages, 4 figures

References in corpus (3)

• Optimal sequence for Parrondo games
• Reversals of chance in paradoxical games
• Parrondo games with spatial dependence and a related spin system, II