Abstract
In this paper, we investigate coevolution of strategy
and structure in Prisoner’s Dilemma. We concentrate on
the noise effect in the topological evolution on cooperation.
We assume individuals can either update their strategies by
imitating their partners or adjust their social ties. At each time
in the strategy evolution, pairwise comparison is employed.
While at each time in the topological evolution, with some
probability, an individual dumps off one of its partner and
makes a new social relationship. We show that a Hamilton-like
rule is obtained, quantitatively saying the more often dissatisfied
links break off than satisfied ones, the more likely cooperation
can prevail, provided the linking dynamics proceeds much
faster than strategy evolution. Furthermore, by investigating
the upper bound of the strategy updating probability, we also
show how much faster linking dynamics proceeds than strategy
evolution to make the Hamilton-like rule valid. Interestingly,
we unveil that the probability is dependent on the frequency
of cooperators. Our work may shed light on the ubiquitous
cooperation in societies.
