Cooperative Parrondo's Games on a Two-dimensional Lattice

TL;DR

This paper investigates cooperative Parrondo's games on a two-dimensional lattice using simulations and Markov chain models, revealing paradoxical outcomes near voter model probabilities and dependence on player count.

Contribution

It extends the analysis of Parrondo's paradox to two-dimensional lattices, providing exact transition probabilities and exploring practical implications.

Findings

Paradox occurs near voter model probabilities

Winning depends on the number of players

Exact transition probabilities are derived for the model

Abstract

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.