Parrondo Games with Spatial Dependence, III

摘要

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 <= N <= 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.