Evolutionary snowdrift game with disordered environments in mobile societies

We investigate an evolutionary snowdrift game on a square $N=LtimesL$ lattice with periodic boundary conditions, where a population of$n_{0}$ ($n_{0}leq N$) players located on the sites of this latticecan 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 disorderedstructures. When $p>0$, the effect of mobility on cooperationremarkably depends on the payoff parameter $r$ and the density ofindividuals $rho$ ($rho=n_{0}/N$). Compared with the results of$p=0$, for small $r$, the persistence of cooperation is enhanced atnot too small values of $rho$; whereas for large $r$, theintroduction of mobility inhibits the emergence of cooperation at any$rho<1$; for the intermediate value of $r$, the cooperativebehaviour is sometimes enhanced and sometimes inhibited, depending onthe values of $p$ and $rho$. In particular, the cooperator densitycan reach its maximum when the values of $p$ and $rho$ reach theirrespective optimal values. In addition, two absorbing states of allcooperators and all defectors can emerge respectively for small andlarge $r$ in the case of $p>0$.