Parrondo Games with Two-Dimensional Spatial Dependence

Parrondo games with one-dimensional (1D) spatial dependence were introduced by Toral and extended to the two-dimensional (2D) setting by Mihailović and Rajković. [Formula: see text] players are arranged in an [Formula: see text] array. There are three games, the fair, spatially independent game [Formula: see text], the spatially dependent game [Formula: see text], and game [Formula: see text], which is a random mixture or non-random pattern of...