1997/10/10 by György Szabó, Gyorgy Szabo, Csaba Tőke +1 · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · Social Sciences · #Combinatorics #Condensed matter physics #Critical exponent #Directed percolation #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Game theory #Ising model #Lattice (music) #Mathematical economics #Mathematics #Opinion Dynamics and Social Influence #Physics #Prisoner's dilemma #Square lattice #Statistical physics #Stochastic game #Temptation #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.58.69
published as Phys. Rev. E, 58 (1998) 69 · 6 pages including 6 figures
arxiv created 1997/10/10 · openalex publication_date 1998/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference. Using Monte Carlo simulations and dynamical cluster techniques, we study the density c of cooperators in the stationary state. This system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect. In the limits \stackrel\ensuremath→c0 and 1 we have observed critical transitions belonging to the universality class of directed percolation.