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that non-monotonic behaviour in the form of non-monotonic offer curves and
utility sequences can easily emerge at any time as a result of the
dynamic effects
of an agent system in which the agents use mixed strategies
involving behaviour-
dependent and -independent tactics
1
. In other words, such a system created
by negotiating agents using mixed strategies may generate non-monotonic be-
haviour even when strategy settings and mixing weights of both agents are
static
and all involved tactics are cooperative in that their individual concession be-
haviour is monotonic. As a result, the agent's own aggregated utilities over all
negotiated issues can be non-monotonic as well, implying that it proposes offers
increasing its own overall utility. These effects are often considered undesirable
for automated single- and multi-issue negotiations [9] [4] as they may delay final
agreements, have significantly varying outcomes with lower utilities, or result
in a partial loss of the agents' control over their strategy due to the high sen-
sitivity of parameters. In this paper, we therefore provide examples as well as
an analysis and evaluation of the traditional mixing method with respect to
the self-emergence of non-monotonic behaviour in the implied negotiation pro-
cess. In particular, we propose two alternative mixing mechanisms based on
linear weighted combination of tactics that solve this problem: the first using
individual imitative negotiation threads, and the second combining individually
proposed concessions of each tactic involved. We prove that both methods avoid
these dynamic effects and ensure monotonic behaviour, the first for static and
the second for dynamic weights. We further demonstrate by means of a com-
parative experimental evaluation that the proposed mechanisms provide utility
gains for both parties in many negotiation settings.
In the next section, we briefly introduce the basic model as well as pure
and mixed tactics for agent-based bargaining and discuss the emergence of non-
monotonic behaviour in multi-tactic strategies. The two alternative mixing mech-
anisms are proposed in Section 3, while the results of an experimental evaluation
are given in Section 4. Related work is presented in Section 5, and, finally we
conclude in Section 6.
2
Mixing Negotiation Tactics
The negotiation model we consider in this paper has been introduced in [4] where
two agents
exchange offers and counteroffers on a number of real-valued
issues such as price or delivery time. The sequence of all offers exchanged between
agents
a
and
b
a
and
b
until time
t
n
is termed a negotiation thread:
X
t
a↔b
x
t
a↔b
x
t
a→b
,x
t
b→a
,x
t
a→b
,...,x
t
b→a
=(
)
i
=1
,...,n
=(
)
.
(1)
x
t
n
b→a
t
n
The offer
at time
indicates the last element of the negotiation thread
t
i
t
i
+1
>t
i
i
,
,...,n
where
represent discrete time points where
with
=1
2
and
n ∈
N
. The next counteroffer of agent
a
given the thread is then
x
t
n
+1
a→b
. We assume
that each agent has a negotiation interval
D
j
=[
min
j
,max
j
]foreachissue
j
1
This paper is a major extension of [10].
