Information Technology Reference
In-Depth Information
C
=
D
= 1.0
D
C
1.0
(1)
C
= 0.0,
D
= 0.0
C
= 0.0,
D
= 1.0
C
= 0.5,
D
= 1.0
C
= 1.0,
D
= 1.0
C
= 1.0,
D
= 0.5
C
= 1.0,
D
= 0.0
(2)
(3)
0.8
y
f
s
(4)
0.6
(5)
(1)
(2)
(3)
(4)
(5)
(6)
(6)
0.4
0.2
0.0
1.0
1.5
2.0
2.5
1.0
1.5
2.0
2.5
T
(
S
= 1 -
T
)
T (S = 1 T)
Fig. 16.8. The eect of a strategy-dependent willingness to change on the nal frequency
of cooperators. Results show the fraction of evolutionary runs ending in 100% of cooperating
individuals, starting from 50% of each strategy, and this in relation to the game parameter T.
The other game parameter S is chosen such that T + S = 1 is satised, bringing us into the
realm of the PD. The situation in which all individuals are equally willing to react to adverse
ties (
C
=
D
= 1:0) serves as a baseline. Reducing
D
makes it easier for Cs to wipe out Ds.
Reducing
C
, on the other hand, has the opposite eect (W = 2:5, N = 10
3
, z = 30, = 0:005).
Hence, both individuals have the opportunity for a unilateral decision. Taken
together, A's decision prevails with probability q
A
=
A
B
p +
A
[1
B
] and
B's decision with probability q
B
=
A
B
(1 p) +
B
[1
A
]. Finally, the link
remains untouched with probability (1
A
)(1
B
), since no individual competes
for the link. This last possibility encompasses the situation in which the social tie
is maintained despite, e.g. mutual dissatisfaction. Overall, introduces a simple
means to study the evolution of each individual's willingness to sever adverse ties.
On the one hand, when all individuals have = 0, no links are rewired, reducing
the population to a static society. On the other hand, when is maximal (= 1),
the limits investigated in the previous section are recovered.
16.4.2. Numerical results
We start by associating the topological strategy of an individual with her strategy
in the game. This means that individuals with the same game strategy will also
have the same topological strategy. In the active linking model of Section 16.2, this
is also included, as we assume that the propensity to form links and the lifetime of
links is determined by the strategies.
When Ds are less eager to change partner (
D
= 0:5 and
D
= 0:0) than Cs
(
C
= 1:0), cooperators ensure the stability of favorable interactions while avoiding
