Promotion of cooperation induced by nonlinear attractive effect in spatial Prisoner's Dilemma game

¹ Institute of Theoretical Physics, Lanzhou University Lanzhou Gansu 730000, PRC
² Department of Electronic Engineering, City University of Hong Kong Kowloon, Hong Kong, PRC

Received: 17 April 2006
Accepted: 18 October 2006

Abstract

We introduce nonlinear attractive effects into a spatial Prisoner's Dilemma game where the players located on a square lattice can either cooperate with their nearest neighbors or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbors with a probability proportional to denoting the attractiveness of the neighbor, where is the payoff collected by it and α (≥0) is a free parameter characterizing the extent of the nonlinear effect; and then adopting its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density of cooperators in the stationary state for different values of α. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect. In particular, for large values of α, i.e., strong nonlinear attractive effects, the system exhibits two absorbing states (all cooperators or all defectors) separated by an active state (coexistence of cooperators and defectors) when varying the temptation to defect. In the critical region where goes to zero, the extinction behavior is power-law–like ~ , where the exponent β accords approximatively with the critical exponent () of the two-dimensional directed percolation and depends weakly on the value of α.