Issue
Europhys. Lett.
Volume 76, Number 6, December 2006
Page(s) 1214 - 1220
Section Interdisciplinary physics and related areas of science and technology
DOI http://dx.doi.org/10.1209/epl/i2006-10381-4
Published online 16 November 2006
Europhys. Lett., 76 (6), pp. 1214-1220 (2006)
DOI: 10.1209/epl/i2006-10381-4

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

J.-Y. Guan1, Z.-X. Wu1, Z.-G. Huang1, X.-J. Xu2 and Y.-H. Wang1

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 in final form 18 October 2006
published online 16 November 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 $\mathcal{A}^\alpha$ denoting the attractiveness of the neighbor, where $\mathcal{A}$ is the payoff collected by it and $\alpha$ ($\geq$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 $\rho_C$ of cooperators in the stationary state for different values of $\alpha$. 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 $\alpha$, 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 $\rho_C$ goes to zero, the extinction behavior is power-law-like $\rho_C$ ~ $(b_c-b)^{\beta}$, where the exponent $\beta$ accords approximatively with the critical exponent ( $\beta\approx0.584$) of the two-dimensional directed percolation and depends weakly on the value of $\alpha$.

PACS
87.23.Kg - Dynamics of evolution.
02.50.Le - Decision theory and game theory.
87.23.Ge - Dynamics of social systems.

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