Figure 1.

Effects of the group size (n) and number of rounds (m) on the evolutionary stability of TFT_n−1 and ALLD when N is large. The parameter space is divided into the following four regions: (i) TFT_n−1 is ESS_N and ALLD is not ESS_N; (ii) both TFT_n−1 and ALLD are ESS_N and ${\rho }_{{\text{TFT}}_{n-1}}>{\rho }_{\text{ALLD}}$; (iii) both TFT_n−1 and ALLD are ESS_N and ${\rho }_{{\text{TFT}}_{n-1}}<{\rho }_{\text{ALLD}}$; and (iv) TFT_n−1 is not ESS_N and ALLD is ESS_N. (a) The situation when b/c=const. Evolution of cooperation becomes more difficult as the group size increases. The parameter value used is b/c=1.5. (b) The situation when b/(nc) =const. Maintenance of cooperation becomes easier with increasing group size. The parameter value used is b/(nc) =0.51.