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q
B
q
A
A decides
B decides
0
0
σ
A
σ
B
p
σ
A
(1-σ
B
)
1 - q
A
- q
B
σ
B
(1-σ
A
)
σ
A
σ
B
(1-p)
A
B
unilateral
decision
nothing
happens
unilateral
decision
competition
competition
Fig. 16.7. Decision on whose preference (either redirect the link when dissatised or maintain the
link when satised) prevails in case of unilateral or mutual dissatisfaction among the interacting
individuals A and B. The dierent colors indicate the three possible outcomes of the rewiring
competition between the two individuals. First, as each individual competes for the link with
probability given by her parameter , A and B compete both with probability
A
B
(indicated
by the hatched zones). In this case, decision is determined by the payo-dependent probability
p (see Eq. (16.6)). Second, when only one of the individuals competes (indicated by the gray
zones), this individual takes a unilateral decision. In total, A's preference prevails with probability
q
A
=
A
B
p +
A
[1
B
], B's preference with probability q
B
=
A
B
(1p) +
B
[1
A
].
Finally, the white zone indicates the situation in which both individuals refuse to compete, such
that the link remains unchanged.
is expected to dominate, although the model could easily be applied to SH and
SG games as well. Since S 1 and T 0, every individual prefers interacting
with cooperators to interacting with defectors. Consequently, everyone attempts
to maintain links with cooperators, but change links with defectors. However, un-
like before, individuals are now not necessarily equally willing to engage in these
conicts. We represent their eagerness to do so by introducing an individual charac-
teristic 2 [0; 1]. Individuals with lower values of will be more resilient to change,
and hence can also be viewed as more loyal towards their interaction partners. In
this way, the behavior of each individual is uniquely dened by two parameters: the
game strategy (C or D) and the topological strategy (). Note that these quanti-
ties are both transferred during strategy update. Thus, both aspects of a players
strategy are subject to evolution and change over time.
Figure 16.7 illustrates how inuences the rewiring decisions. Consider two
connected individuals A and B, whose topological strategies are given by
A
and
B
. A potential conict about the link arises as soon as at least one of the individ-
uals is dissatised about the interaction. If this is the case, both A and B decide
independently of each other whether they will compete for the link or not. Each
individual competes with probability given by her topological strategy . As such,
A
and
B
dene three possible outcomes for the competition over the link between
A and B. First, both A and B compete for the link with probability
A
B
. The
individuals' payos
A
and
B
ultimately dictate the winner of this conict. The
decision of A prevails with probability p = [1 + e
[
A
B
]
]
1
, the decision of B
with probability 1 p. If decision is to redirect the link, the new partner is chosen
randomly from the immediate neighbors of the former partner. Second, A competes
while B does not with probability
A
[1
B
]. In this case, A decides the fate of the
link unilaterally. Similarly, when B competes but A does not (this happens with
probability
B
[1
A
]), B decides the fate of the link unilaterally.
