Phase transition in random walks coupled with evolutionary game

¹ College of Physics and Electronic Engineering, Guangxi Teacher Education University - Nanning 530001, China
² School of Engineering Science, University of Science and Technology of China - Hefei 230026, China
³ Department of Modern Physics, University of Science and Technology of China - Hefei 230026, China

^a sxy11@mail.ustc.edu.cn

Received: 19 August 2010
Accepted: 27 September 2010

Abstract

We investigate a non-equilibrium process of random walk coupled with evolutionary game on one-dimensional periodic lattices. A first-order phase transition is observed, i.e., the cooperator ratio suddenly decreases at a critical density ρ_cr. The defector ratio remains constant when the density ρ>ρ_cr, but it decays exponentially when ρ<ρ_cr. The behavior is compared with that studied by Barato and Hinrichsen (Phys. Rev. Lett., 100 (2008) 165701). The evolution of cooperator ratio and the system flux have also been studied via Monte Carlo simulation and mean-field analysis.