We have studied a spatially extended
snowdrift game, in which the players are located on the sites of
two-dimensional square lattices and repeatedly have to choose one of the two strategies, either cooperation (C) or defection (D).
A player interacts with its nearest neighbors only, and
aims at playing a strategy which maximizes its instant pay-off,
assuming that the neighboring agents retain their strategies.
If a player is not content with its current strategy, it will change
it to the opposite one with probability p next round. Here we show through simulations and analytical approach that these rules result in cooperation levels, which differ
to large extent from those obtained using the replicator dynamics