Spatial snowdrift game in heterogeneous agent systems with co-evolutionary strategies and updating rules*
Xia Hai-Jiang, Li Ping-Ping, Ke Jian-Hong†, Lin Zhen-Quan
       
The relative cooperation frequencies g ca and g cb versus the cost-to-benefit ratio r at ν T = 36. It is shown that both g ca and g cb have a discontinuous steplike structure for each initial composition f a 0. g cb decreases with f a 0 in the range of 0 < r < 1/2, while it consistently equals zero in the range of 1/2 < r < 1. g ca always has a non-zero value for arbitrary r . Moreover, with increasing f a 0 f c first increases and then decreases in the range of 0 < r < 1/2, and it consistently decreases with the increase of f a 0 in the range of 1/2 < r < 1.