FIG. 3.
(color online). Co-evolutionary dynamics of strategy and structure. The curves drawn correspond to the results of computer simulations carried out for networks of size N = 100. Parameters and payoff matrices are the same as in Fig. 2. The rescaled payoff-matrix leads to a fixed point at a fraction of cooperators NC/N ≈ 35%. For each value of the ratio Ts/Ta, we ran 100 simulations, starting from 50% cooperators and a complete graph. The values plotted correspond to the fraction of runs which ended with 100% cooperators. We fix Ts = 1 and vary Ta. In each time step, synchronous updating of strategies is carried out with probability Ta/(Ts + Ta) using Fermi-update, AL beeing carried out otherwise. For the extreme limits we obtain perfect agreement with the analytic predictions. However, the analytic results remain valid for a much larger range of values 0.01 ≤ Ta/Ts ≤ 0.1 than one would expect from pure theoretical considerations. Indeed, only between these two limits a crossover takes place, which depends on the intensity of selection β as illustrated.