ring networks or random lattice networks. Three different starting lattice networks are used: regular square lattices ($k=4$), triangular lattices ($k=6$) and square lattices where each node is connected to its Moore neighbourhood ($k=8$). For all values of $k$ ring networks can be considered as one-dimensional because for a given cluster of nodes the size of the surface is independent of the volume whereas for lattice network the relationship is $V
\approx S^2$.

Throughout our simulations, we have considered two types of evolutionary dynamics, one deterministic [@sza2] and the other stochastic [@oht]. In both cases, each player either copies the strategy of one of its neighbours or sticks to the same strategy used in the previous round. In the deterministic dynamics each player copies the strategy of its most successful neighbour, if the payoff of that neighbour is larger than its own. In the probabilistic dynamics, previously used in [@oht], it copies the strategy of a neighbour chosen at random, with a probability proportional to its relative payoff. His own strategy is also included in the pool of eligible strategies. As the results we have obtained are qualitatively the same for both types of dynamics, in the following we focus on 