2006/11/16 by Jian-Yue Guan, Jian‐Yue Guan, Zhi-Xi Wu +6 · 68 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · Social Sciences · #Critical exponent #Directed percolation #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Exponent #Game theory #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical economics #Mathematics #Nonlinear system #Physics #Prisoner's dilemma #Scaling #Statistical physics #Stochastic game #Temptation #physics.soc-ph
paper · pdf · doi:10.1209/epl/i2006-10381-4
published in Europhysics Letters (EPL) 76(6), 1214-1220 (Institute of Physics) · 7 pages, 4 figures
openalex publication_date 2006/11/16 · arxiv created 2007/01/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/09
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 α 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 ρ C 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 ρ C goes to zero, the extinction behavior is power-law–like ρ C ( b c − b ) β , where the exponent β accords approximatively with the critical exponent (β ≈ 0.584) of the two-dimensional directed percolation and depends weakly on the value of α.