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For efficiency, the agent should choose the topics so as to minimise the expected number
of steps. From our observations about what is conversationally implied in persuasion
dialogues, we conjecture that an optimal strategy,
S
for an agent would be to inquire
about attributes in descending order of their weights, and so employing a kind of greedy
algorithm. We now present the protocol and embedded strategy
for our persuasion
dialogue. Agents can
open
and close the relevant dialogues,
propose
options and
inquire
about the status of attributes, as in [2]. A persuasion dialogue follows the following
protocol:
S
[P0]: Wilma opens by proposing an option,
O
2
. If Bert's currently preferred option
is
O
1
=
O
2
a persuasion dialogue will commence; otherwise he agrees immedi-
ately. Initially
A
=
X
=
∅
;
W
= the set of weights of all attributes about which
Bert may inquire.
[P1]: Bert opens inquiry dialogues with topics
τ
1
j
,τ
2
j
for some attribute
a
j
with
which Bert associates a positive weight
w
j
;
A
becomes
A ∪{a
j
}
;
X
becomes
X ∪{w
j
}
; increment the utilities
U
i
:
i ∈{
1
,
2
}
by
τ
ij
w
j
. This may change which
option is currently preferred.
[P2]: If
T
2
(
X
)
hold terminate with
O
2
preferred else if
X
=
W
, return the currently preferred option; else go to [P1].
The inquiry about a single attribute in [P1] and [P2] is termed a
step
. Moves are sub-
scripted with
W
or
B
depending on whether the move is made by the agent acting as
the persuader (
W
) or persuadee (
B
). There are two options
O
1
and
O
2
. Thus the dia-
logue begins with
W
proposing
O
2
.Now
B
either agrees, or states its preferred option
and inquires about some attribute. Since only
B
's weights matter,
w
j
will refer to the
weight given to
a
j
by
B
.
T
1
(
X
)
holds terminate with
O
1
preferred, else if
open dialogue
W
propose
W
(
O
2
)
if
agree
B
(
O
2
)
)
T
2
(
∅
)
,
end dialogue
B
else
X
=
∅
propose
B
(
O
1
)
, such that
O
2
∅
;
A
=
=
O
1
open persuasion dialogue
B
for all
a
j
∈
A
O
do
sort
A
O
into ordered descending list such that
w
j
≥
w
j
+1
end for
j
=1
while
¬T
2
(
X
)
do
inquire
B
(
τ
1
j
,τ
2
j
)
A
becomes
A
¬T
1
(
X
)
and
∪{
a
j
}
;
X
becomes
X
∪{
w
j
}
;
increment the utilities
U
i
:
i
∈{
1
,
2
}
by
τ
ij
w
j
.
if
τ
1
j
=1
then
a
j
∈
VT
1
else
a
j
∈
VF
1
end if
if
τ
2
j
=1
then
a
j
∈
VT
2
else
a
j
∈
VF
2
end if
