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convince a risk-taking agent. Since some ultimatum choices amongst various justified sets
of alternatives are not always possible, we will consider in this paper the most “skeptically
preferred” decisions.
The decision making process can be described as the cognitive process in which an agent
evaluates the alternatives that are available, according to their features, to determine whether
and how they satisfy his needs. The principle for decision making we adopt is that
higher-ranked goals should be pursued at the expense of lower-ranked goals, and thus choices
enforcing higher-ranked goals should be preferred to those enforcing lower-ranked goals. We
are in a situation where there is a ranking of individual objects (the preferences between goals)
and we need a ranking that involve subsets of these objects (See Barber et al. (2004) for a
survey). For this purpose, we adopt the minmax ordering.
Definition 18
(Preferences)
.
Let
DF
=
DL
P
I
T
P
RV
,
sm
,
,
,
,
be a decision framework. We
consider
G
,
G
twosetsofgoalsin
and
D
,
D
two sets of decisions in
G
D
.
G
is
preferred
to
G
(denoted
G
P
G
) iff
1.
G
⊃
G
,and
2.
∈
G
\
G
there is no g
∈
G
such that g
P
∀
g.
D
is
credulously preferred
(respectively
skeptically preferred
)to
D
(denoted
D
P
g
c
D
and
D
P
s
D
) iff
(
D
)
(
D
)
(
D
)
P
val
c
(
D
)
P
val
s
val
c
(respectively
val
s
).
Formally, let
SAD
=
{
D
|
D
⊆D
such that
RV ⊆
val
s
(
D
)
and
∀
D
⊆D
(
D
)
(
D
)
P
val
s
(
D
)
}
be the set of decisions which can be skeptically accepted by the agent. Additionally, let
SAG
=
{
it is not the case that
RV ⊆
val
s
and
val
s
∈SAD}
be the goals which can be skeptically reached by the agent.
As an example of the decision making principle, consider the goals
g
0
,
g
1
and
g
2
such that
g
2
P
|
⊆G
such that
G
=
(
)
with
D
G
G
val
s
D
g
1
,
g
2
P
g
0
and
RV
=
{
g
0
}
.
{
g
2
,
g
1
,
g
0
}
is preferred to both
{
g
2
,
g
0
}
,
{
g
2
,
g
1
}
whereas
{
g
2
,
g
0
}
,
{
g
2
,
g
1
}
are incomparable and so equally preferred. However,
{
g
2
,
g
1
}
cannot be
reached by the agent since it does not includes the reservation value.
Let us consider now the buyer's decision problem in the procurement example.
Example 7
(Semantics)
.
The structured argument
¯
Cand D
2
, which are depicted in Fig. 1 and Fig. 2,
conclude
fast
. Actually, the sets of decisions
{
s
(
c
)
}
and
{
s
(
d
)
}
credulously argue for f ast. The
decisions
{
s
(
d
)
}
skeptically argue for
cheap
and a fortiori credulously argue for it. Therefore,
{
s
(
d
)
}
is a skeptically acceptable set of decisions. The reservation value of the buyer only contains
fast
. Therefore,
{
s
(
d
)
}
{
s
(
c
)
}
{
s
(
d
)
}
is skeptically preferred to
and
is a skeptical acceptable set of
decisions due to the reservation value and the priority over the goals.
In our example, there is only one suggested set of decisions.
Since agents can consider multiple objectives which may not be fulfilled all together by a set of
non-conflicting decisions, they may have to make some concessions, i.e. surrender previous
proposals. Concessions are crucial features of agent-based negotiation. Jeffrey S. Rosenschein
and Gilad Zlotkin have proposed a monotonic concession protocol for bilateral negotiations
in Rosenschein & Zlotkin (1994). In this protocol, each agent starts from the deal that is best for
him and either concedes or stands stills in each round. A (monotonic) concession means that
an agent proposes a new deal that is better for the other agent. Differently from Rosenschein &
Zlotkin (1994), we do not assume that the agent has an interlocutor and if it does, that it does
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