Abstract
Abstract In this paper, we study numerically the prisoner’s dilemma game (PDG) and snowdrift game (SG) on a two-dimensional square lattice with both quenched and annealed bond dilution. For quenched bond dilution, the system undergoes a dynamical transition at the critical occupation probability q ∗ , which is higher than the bond percolation transition point for a square lattice. In the critical region, the defined order parameter has a scaling form as P e ∼ ( q − q ∗ ) β for q q ∗ with the critical exponents β = 1.42 for PDG and β = 1.52 for SG, which differ from those with quenched site dilution. For annealed bond dilution, the system exhibits a distinct cooperative behavior. We find that the cooperation is much enhanced in the range of small payoff parameters on a lattice with slightly annealed bond dilution.
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