Information Technology Reference
In-Depth Information
Fig. 16.4. Readjusting social ties. Cooperators and defectors interact via the links of a network.
B is satised, since A is a cooperator (T > 0). On the other hand, A is unsatised with this
situation (S < 1). Therefore, A wants to change the link whereas B does not. The action taken is
contingent on the tness
A
and
B
of A and B, respectively. With probability p (see Eq. (16.6)),
A redirects the link to a random neighbor of B. With probability 1p, A stays linked to B.
Finally, if both players are dissatised, the same methodology is used to decide who keeps the
connection.
Because S 1 and T 0, the payo against a cooperator is always higher than
the payo against a defector, cf. Eq. (16.13). Thus, interacting with a cooperator
is always the best possible option. Consequently, every individual will be satised
when connected to a C and dissatised otherwise. Keeping the total number of
links constant, all individuals are now able to decide, on an equal footing, those
ties that they want to maintain and those they want to change. The co-evolution
between strategy and network structure is therefore shaped by individual prefer-
ences towards interacting with one of the two strategies [Santos et al. (2006a)].
Figure 16.4 illustrates the process. If A is satised, she will decide to maintain the
link. If dissatised, then she may compete with B to rewire the link (see Fig. 16.4),
rewiring being attempted to a random neighbor of B. Thus, the loser in a com-
petition for a link loses an interaction. This paves the way for the evolution of a
degree-heterogeneous network. The intuition behind this reasoning relies on the
fact that agents, equipped with limited knowledge and scope, look for new social
ties by proxy [Kossinets and Watts (2006)]. Such a procedure can only be treated
numerically and does no longer lead to a simple rescaling of a payo matrix as
the mechanism discussed in Section 16.2. On the other hand, it introduces some
features characteristic of realistic social networks.
The fact that all individuals naturally seek to establish links with cooperating
individuals, creates possible conicts of interests as illustrated in Fig. 16.4. For
instance, B is satised, because she can prot from A. Obviously, A is not satised
and would prefer to seek for another cooperator. Decision is contingent on the
payo
A
and
B
of A and B, respectively. With probability p = [1+e
[
A
B
]
]
1
(also used in the strategy update, cf. Eq. (16.6)), A redirects the link to a random
neighbor of B. With probability 1p, A stays linked to B. Whenever both A and B
