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where the apex
B
j
means 'believed by
Ag
j
; in fact in this new formula
Ag
j
both
believes
the
number of potential collaborative agents (
l
) and the number of competitors (
p
ki
) for each of
them.
It is clear how, on the basis of these parameters (
l
Bj
and
p
ki
Bj
), the negotiation power of
Ag
j
is
determined. And, at the same time, his own decisions will be strongly influenced. Analogously,
we can interpret Figure 10.5 as the set of relationships among the agents, believed by
Ag
j
.In
this case we take the subjective point of view.
10.2.3 Trust Role in Dependence Networks
We would like to introduce into the dependence network the trust relationship. In fact, the
dependence network alone is not sufficient for a real allocation of tasks among the agents. It
is true that
Ag
i
should be able and willing to realize the action
α
k
: But how? And, will it be
sufficient given my expectations? Would it be more or less trustworthy than
Ag
z
? To answer
these questions the agents in the dependence network have to establish among themselves the
reciprocal trust about the different tasks they can allocate to each other.
Indeed,
although it is important to consider the dependence relationship between agents in
society, there will be not an exchange in the market if there is not the trust to strengthen these
connections
. Considering the analogy with Figure 10.4, we will now look at a representation
as given in Figure 10.7 (where
Set 4
includes the set of agents that
Ag
j
considers trustworthy
for achieving
g
jk
).
We have now a new subset (the dark agents in Figure 10.7) containing the potential agents
for negotiation. By introducing the basic beliefs about trust in the
Subjective Potential for
Negotiation
(of
Ag
j
∈
Agt
and its own goal
g
jk
) we also introduce the superscript index
T
to
differentiate it from the
SPN
without trust and we have:
l
Bj
Bj
Bj
DoA
ik
∗
DoW
ik
SPN
T
(
Ag
j
,
g
jk
)
=
)
(10.5)
1
+
p
ki
Bj
i
=
1
DoA
ik
Bj
,
DoW
ik
Bj
with 1
0.
where
DoA
ik
Bj
and
DoW
ik
Bj
are, respectively, the degree of ability and willingness (with
respect to the goal
g
jk
) of the agent
Ag
i
as believed by
Ag
j
(see Chapter 3). We do not consider
here the potential relations between the values of
DoA
ik
Bj
and
DoW
ik
Bj
with the variable
p
ki
Bj
.
On analyzing Figure 10.7, we can see that there are two other agents (medium dark) that are
trustworthy according to
Ag
j
on the goal
g
jk
but they do not depend on
Ag
j
for something. In
fact the dependence and trust relationships are strongly interwined and not simply sequential
as shown above. Not only does the decision to trust presuppose a belief of being dependent,
but notice that a dependence belief (
BelDep
) implies on the other hand an element of trust. In
fact to believe oneself to be dependent means:
≥
≥
(
BelDep-1
) to believe not to be able to perform action
α
and to achieve goal
g
; and
(
BelDep-2
) to believe that
Ag
i
is
able
and in condition to achieve
g
, performing
α
.
Notice that (
BelDep-2
) is precisely one component of trust in our analysis: the
positive
evaluation
of
Ag
i
as competent, able, skilled, and so on. However, the other fundamental
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