Figure 1. Population dynamics whenever only cooperators and defectors compete to survive.
The intersection of 
with horizontal line 
(dashed line) represents the values of fraction of cooperators 
(if 
exists) at which payoff of cooperators is equivalent to that of defectors, i.e., 
. 
Group's success is inverse-sigmoidally dependent on the cooperativeness of the group. 
Group's success is linearly dependent on the cooperativeness of the group. In these two cases, scenarios with none, a unique interior fixed point are possible as 
changes. 
Group's success is sigmoidally dependent on the cooperativeness of the group. Intriguingly, for this pattern, the population dynamics exhibit very rich dynamics: scenarios with none, one and two interior fixed point are possible as 
changes. Parameters 
and 
, 
, and 
.