Figure 2. Population dynamics whenever cooperators defectors, and loners compete to survive.

The lines embedded with solid triangle, square, and circle represent the evolutionary trajectories of cooperators, defectors and loners, respectively. For , in both the linearly-dependent and sigmoidally-dependent patterns, the evolution share the property that when cooperators abound, it is better to defect, while defectors' prosperity puts the loners in the advantageous place forever, and thus loners take over the whole population. In the inverse sigmoidally-dependent pattern, loners do thrive ensuing the defectors' abundance. An exception emerges while the population consists of most cooperators, it drives to the full cooperative state. Loners win the evolutionary race when the population starts with a state in which cooperators and defectors, and loners have the same share. Parameters , . Upper row , middle row , and low row .