Figure 5. Triangle plots illustrating the population dynamics for defectors (), cooperators () and loners () for trajectories starting from all possible initial frequencies for the inverse-sigmoidal risk removal pattern.

Each vertex represents a homogeneous population of that pure strategy. For small interest rate , except for the unique nontrivial fixed point () located inside the simplex , there also exists another nontrivial fixed point located in the line (). In consequence, the inside area of the simplex is divided into two attraction basins, with one being loners' and the other cooperators'. For modest , and as in plot still exist. Instead the cooperators' attraction basin covers absolutely large fraction of the inside area of the simplex , and loners win the evolution for population starting from the remaining area. If defectors are abundant, the population converges to the full cooperative state in a spiral way around the unstable fixed point . Otherwise, the population directly drives towards . Further increase in continue to expand the cooperators' attraction basin. It should be noted that even , the attraction basin albeit narrow does not vanish. Relevant parameters , and , , .