Cooperative Parrondo's Games on a Two-dimensional Lattice

Cooperative Parrondo's games on a regular two dimensional lattice are analyzed based on the computer simulations and on the discrete-time Markov chain model with exact transition probabilities. The paradox appears in the vicinity of the probabilites characterisitic of the "voter model", suggesting practical applications. As in the one-dimensional case, winning and the occurrence of the paradox depends on the number of players.