Abstract
We investigate an evolutionary snowdrift game on a square N = L × L lattice with periodic boundary conditions, where a population of n0 (n0 ≤ N) players located on the sites of this lattice can either cooperate with or defect from their nearest neighbours. After each generation, every player moves with a certain probability p to one of the player's nearest empty sites. It is shown that, when p = 0, the cooperative behaviour can be enhanced in disordered structures. When p > 0, the effect of mobility on cooperation remarkably depends on the payoff parameter r and the density of individuals ρ (ρ = n0/N). Compared with the results of p = 0, for small r, the persistence of cooperation is enhanced at not too small values of ρ; whereas for large r, the introduction of mobility inhibits the emergence of cooperation at any ρ < 1; for the intermediate value of r, the cooperative behaviour is sometimes enhanced and sometimes inhibited, depending on the values of p and ρ. In particular, the cooperator density can reach its maximum when the values of p and ρ reach their respective optimal values. In addition, two absorbing states of all cooperators and all defectors can emerge respectively for small and large r in the case of p > 0.