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min
j
max
j
where
and
are the initial and reservation values, respectively, if
a
is
a buyer agent whereas the opposite holds for a seller, and
D
j
istheissuedomain
D
j
,D
j
⊆ D
j
. Each agent has a utility function
U
j
D
j
→
with
1] associated
to each issue which assigns a score to the current value within its acceptable
interval. We assume that utility functions are monotonically increasing or de-
creasing depending on the issue and the role of the agent. For example, for issue
price
the utility function is decreasing for a buyer and increasing for a seller. For
each offer
:
[0
,
)=
j
w
j
U
j
(
U
a
(
x
of an agent
a
, the aggregated utility function
x
x
j
)
determines the score for all issues
j
,wheretheweight
w
aj
represents the rela-
with
1
≤j≤p
w
j
tive importance of issue
= 1. Agents may include
discounts or negotiation costs, however, for simplicity we do not consider such
a case here. The agents exchange offers alternately until one agent accepts or
withdraws from the negotiation. An offer is accepted by agent
j
to agent
a
a
if the overall
utility of agent
b
's last offer is equal or higher than
a
's next offer, such that
x
t
n
+1
x
t
b→a
U
a
(
≥ U
a
(
t
a
max
.Even
though the utility structure may be more complex and of a different shape the
functioning of the negotiation strategies described in this paper are best mea-
sured when using above linear utility function. Accordingly, it has been shown
[7] that strategies well-suited for monotonic utility models do not cope well with
non-monotonic utility spaces, so that we restrict to the former.
)
). An agent withdraws if it reaches its deadline
a
2.1 Negotiation Tactics and Strategies
A common method to generate offers is to use tactics or decision functions which
utilize changes in the negotiation environment such as proposals from negotiation
partners, or available resources such as time or the number of negotiating agents.
In particular, a tactic
τ
j
is as a function mapping the mental state (about its
τ
j
environment) of an agent
MS
a
→ D
j
.Typical
examples of such tactics are the time-, resource- or behaviour-dependent tactics
proposed in [4]. A wide range of different negotiation strategies can be created by
an agent through mixing of pure tactics. Faratin et al [4] introduces the concept
of strategies where tactics are mixed based on a weight matrix
a
to the issue domain
D
j
with
:
⎛
⎞
γ
11
γ
12
... γ
1
m
γ
21
γ
22
... γ
2
m
. .
.
.
.
.
γ
p
1
γ
p
2
... γ
pm
⎝
⎠
Γ
t
n
+1
a→b
=
(2)
where
. The weighted linear combina-
tion of tactics is then defined by the weighted sum of proposed offers of each tactic
x
γ
ji
∈
[0
,
1] is the weight of tactic
i
for issue
j
]=
i
=1
γ
ji
· τ
ji
where weights are normalized with
i
=1
γ
ji
=1.The
weighted counterproposal extends the negotiation thread by appending
t
n
+1
a→b
[
j
x
t
n
+1
a→b
whereby each row in the matrix represents a weighted linear combination of
m
tactics for one issue. Different types of negotiation behaviour can be obtained
by weighting a given set of tactics in different ways. For example, the agent's
mental state can change and generate a new weight matrix [3] depending on the
