Information Technology Reference
In-Depth Information
In this model,
p
if
depends on whether an agent A (actor) behaves according to its
concept (event BC), which has probability equal to the initial value of the coefficient
that we set (
c
0
), or not (event NBC, with probability
1 - c
0
). Then, if A acts according
to its concept, then there is a
p
i
probability that A and O share all their conceptual
content (event SACC), and a
1- p
i
probability that they don't share it all (i.e., each has
a different version of the same concept, event NSAAC). If they share all their
conceptual content (with probability
pi
), then it is certain that O will strengthen its
concept's coefficient. If they share versions of the same concept (with probability
1-
p
i
), then it is less than certain (
p(a1)
) that O will strengthen its concept.
On the other hand, if A does not behave according to its concept (event NBC), and
A and O share all their conceptual content (event SAAC, with probability
p
i
), then
O's concept will certainly weaken. Alternatively, if A and O do not share all their
conceptual content (event NSAAC), then it might happen that A provides O with
some portion of the conceptual content, and thus O's concept might strengthen with
probability
p(a2)
.
Solving the probability tree of Figure 5 for
p
if,
we
obtain:
p
p
p
p
p
p
c
c
=
[
+
(
−
)]
+
(
−
)(
1
−
)
.
(1)
0
0
if
i
a
1
i
i
a
2
In (1), remember that
p
i
corresponds to the probability that agents share all their
conceptual content, i.e. that they have the same version of a concept. Thus, we can
calculate
p
i
for the beginning of a run. In such initial condition, we will have
N/V
agents with the same version of a concept, where
N
equals the total number of agents
and
V
is the number of different versions of a concept. Then, the initial probability
that agent O will interact with an agent A that has the same version of the concept will
be equal to the number of other agents that have the same version as O has (without
counting O), divided by the total number of agents (without counting O):
N
−
1
(2)
p
i
V
=
.
N
−
1
For the value of the parameters used in the runs,
N
= 100 and
V
= 5, so that
p
i
= 19/99
= 0.1919.
Now, if we set
p
if
= 0.5
in (1), i.e. the ideal condition for obtaining a bifurcation,
and establish
c
0
= 0.5 (the value we used in our simulation runs), we can get equation
(3), which states the ideal condition for
p(a1)
and
p(a2)
for getting a bifurcation.
p
p
+
=
1
.
0
.
(3)
a
1
a
2
Note that (3) does not contain
p
i
,
which means that that condition applies for any
value of
p
i
. Equation (3) corresponds to a line with an intercept with the y axis (
p(a2)
axis) equal to 1.0 and slope equal to -1.0, which coincides with the line depicted in
Figure 4 that represents the combinations of
p(a1)
and
p(a2)
where we obtained a
bifurcation. Now, if the sum of
p(a1)
and
p(a2)
is bigger than 1.0, we obtain a parallel
line to (3), but located above (3). In that case,
p
if
is larger than 0.5, and thus most
