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We define
Dependence-Network(Agt,t)
the set of dependence relationships (both subjective
and objective) among the agents included in
Agt
setatthetime
t
. Each agent
Ag
j
∈
Agt
must
have at least one dependence relation with another agent in
Agt
.
More formally, a dependence network of a set of agents
Agt
at the time
t
can be written:
Dependence
-
Network
(
Agt
,
t
)
=
Obj
-
Dependence
(
Ag
j
,
Ag
i
,
g
jk
)
(10.1)
∪
Subj-
Dependence
(
Ag
j
,
Ag
i
g
jk
)
with Ag
j
,Ag
j
∈
Agt.
10.2.2 Dependence and Negotiation Power
Given a
Dependence-Network(Agt,t)
, we define
Objective Potential for Negotiation
of
Ag
j
∈
Agt
about its own goal
g
jk
- and call it
OPN(Ag
j
,
g
jk
)
- the following function:
f
l
1
OPN
(
Ag
j
,
g
jk
)
=
(10.2)
1
+
p
ki
i
=
1
Where:
f
is in general a function that preserves monotonicity (we will omit this kind of function in
the next formulas);
l
represents the number of agents in the set
Agt
that have an objective dependence relation
with
Ag
j
with respect to
g
jk
(this dependence relation should be either reciprocal or mutual: in
other words, there should also be an action, plan, or resource owned by
Ag
j
that is necessary
for the satisfaction of any of
Ag
i
's goals);
p
ki
is the number of agents in
Agt
that are objectively requiring (there is an analogous
dependence relation) the same actions/plans/resources (as useful for
g
jk
)to
Ag
i
on which is
based the dependence relation between
Ag
j
and
Ag
i
and that in consequence are competitors
with
Ag
j
actions/plans/resources in an incompatible way (
Ag
i
is not able to satisfy all the
agents at the same time: there is a saturation effect). See Figure 10.4 for an example.
So, in case there are no competitors with
Ag
j
(
p
ki
=
0
for each
i
∈
{
1,
...
,l
}
)
we have:
f
l
1
OPN
(
Ag
j
,
g
jk
)
=
=
l
(10.3)
1
+
p
ki
i
=
1
More precisely, this
Objective Potential for Negotiation
should be normalized and evaluated
with respect to each of the potential required tasks (actions, plans, resources) for the goal in
object (
g
jk
): in fact, the achievement of this goal could require different performances of the
dependent agents (see, for example, Figure 10.5:
Ag
j
needs
A
,
B
and
C
to achieve its goal
g
jk
).
In the dependence network there are three agents.
Ag
1
can offer
A
and
B
and can exploit
N
by
Ag
j
;
Ag
2
can offer
A
and
C
and can exploit
L
by
Ag
j
;
Ag
3
can offer
B
and can exploit
N
by
Ag
j
.
Finally,
Ag
2
is concurrent with
Ag
j
on
B
with both
Ag
1
and
Ag
3
(see also Figure 10.4).
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