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(T < 1:8), the incentive to change is low since many social ties rely on mutual
satisfaction. Hence, the distribution of over all individuals hardly changes. For
higher values of T (1:8 T 2:1) a transition occurs from cooperator dominance
to defector dominance. Competition becomes erce and it pays to respond swiftly
to adverse ties, as evidenced by an increase of C() in Fig. 16.9. Ds are, however,
subject to a much stronger pressure to change their links than Cs, since they can
never establish social ties under mutual agreement. Thus, only Ds with high
survive. As a consequence, defectors end up to react promptly to adverse ties,
whereas cooperators will always be rather resilient to change. For even larger values
of T (> 2:1), defection dominates and evolutionary competition of linking dynamics
fades away. As a result, the incentive to increase swiftness reduces, a feature which
is indeed reected in the behavior of C().
16.5.Discussion
Our analysis has been limited to one-shot games. In other words, individuals in-
teract once during the lifetime of a link as if they have never met before. But
in repeated interactions, more possibilities exist. If I only take into account your
behavior in the last interaction, there are already 2
2
= 4 strategies. Since the num-
ber of strategies grows rapidly with memory [Lindgren (1991); Ebel and Bornholdt
(2002b)], one often considers so called trigger strategies in which individuals keep
their behavior unchanged until they are faced with an unsatisfactory partner for the
rst time. Such strategies can be implemented into our active linking framework,
assuming that individuals act repeatedly as long as a link between them is present.
This procedure leads to analytical results for evolutionary stability under active
linking even in the context of repeated games [Pacheco et al. (2008)].
Other studies have shown numerically that network dynamics can signicantly
help dominated strategies. Even if only the dominant strategy can locally aect the
network structure, this can help the dominated strategy under certain linking rules
that put restrictions on mutual interactions of the dominant strategy [Zimmermann
et al. (2005); Zimmermann and Egu luz (2005); Biely et al. (2007)]. A recent study
for growing networks has shown that the defectors in the PD have an advantage as
long as a network is growing by preferential attachment. Once network growth is
stopped, the cooperator strategy increases in frequency [Poncela et al. (2008)].
To sum up, by equipping individuals with the capacity to control the number,
nature and duration of their interactions with others, we introduce an adaptive
network dynamics. This leads to surprising and diverse new game dynamics and
realistic social structures. We have presented approaches of how to implement net-
work dynamics. The rst one, active linking, allows to dene dierential equations
for the numbers of links, which leads to analytical results. The second approach, in-
dividual based linking dynamics, is implemented numerically and leads to network
features of empirical social networks.
Both cases provide a clear and insightful
