the deterministic dynamics, and comment briefly on the small differences obtained when using the stochastic dynamics

Numerical Results
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As mentioned in the previous section, we consider two different dynamics, though explicit results corresponding to only one of them will be shown in the following paragraphs. In all the cases we consider regular networks with 1000 to 10000 nodes with even degrees between 4 and 8. We observe no dependence on the size but different regimes associated to the degree. The state of the nodes is synchronically updated and the payoff of each player is not cumulative in time. Even though we observe that different initial concentrations of cooperators, $\rho_c(0)$, lead to qualitatively the same results, when properly scaled, there are some important differences. To show this we use two different initial concentrations of cooperators, $\rho_c(0)=0.1$ and $\rho_c(0)=0.5$ for every network analyzed in this paper.

If the equilibrium value of $\rho_c$ is plotted as a function of $t$, leaving all the other parameters constant, a piecewise constant function is obtained as is shown in Fig.1. This has also been previously noticed [@dur], but with a different payoff table (in the case considered in [@dur] a cooperator gets $0$ payoff when 