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which the frequency of cooperators crosses 50%). Thus, the evolutionary outcome
and eective game at stake relies on the capacity of individuals to adjust to adverse
ties.
Figure 16.6 also provides evidence of the detailed interplay between strategy
and structure. On one hand, strategy updating promotes a local assortment of
strategies, since Cs breed Cs and Ds breed Ds. On the other hand, under struc-
tural updating, one is promoting local assortative interactions between cooperators
(that is, CC-links) and disassortative interactions between defectors and coopera-
tors (that is, CD-links), which constitute favorable steps for cooperators, from an
individual point of view. Clearly, when simultaneously active, strategy update will
reinforce assortativity among Cs, but will inhibit disassortativity between Ds and
Cs, which overall will promote the dominance of cooperation over defection.
16.3.3. Graph structures under individual based linking dynamics
For any W > 0, individual choices lead to heterogeneous graphs in which some
individuals interact more and more often than others. The overall onset of increase
of heterogeneity qualitatively follows the wave of cooperation dominance shown in
Fig. 16.5 [Santos et al. (2006a)]. In fact, the overall heterogeneity of the graph in-
creases as W increases reaching a maximum at W
critical
, above which heterogeneity
decreases again down to a stationary value determined by neutral dynamics in a
system with one strategy only [Santos et al. (2006a)]. The results shown suggest
that the adaptive dynamics of social ties introduced here coupled with social dilem-
mas accounts for the heterogeneities observed in realistic social networks [Amaral
et al. (2000)].
16.4.LocalLinkingwithIndividualLinkingTimeScales
In the two previous models, the linking dynamics proceeds population-wide at the
same speed, determined by W. This implies that all individuals are assumed to
react in the same way to adverse social ties. It is commonly observed, however,
that dierent individuals respond dierently to the same situation [Rubin (2002);
Ridley (2003); Buchan et al. (2002)] | some have the tendency to swiftly change
partner, whereas others remain connected even though they are dissatised with
their partners' behavior. Extending the linking dynamics introduced in the previous
section allows us to represent this kind of behavioral diversity [Van Segbroeck et al.
(2008, 2009)].
16.4.1. Specication of the linking dynamics
We adopt the same parameterization of 2 2 games as in Section 16.3 and x the
dierence between mutual cooperation and mutual defection to 1, making R = 1
and P = 0. We focus on the PD in which S < 0 and T > 1, i.e. when defection
