An Efficient Technique for Detecting Time-dependent Tactics
in Agent Negotiations
Jakub Brzostowski
1
and Ryszard Kowalczyk
2
1
Institute of Mathematics, Silesian University of Technologz, ul. Kaszubska 23, Gliwice, Poland
2
Faculty of Information and Communication Technologies, Swinburne University of Technology,
John St, Hawthorn, Australia
Keywords:
Negotiation, Negotiation Tactic, Tactic Detection.
Abstract:
The paper proposes an efficient technique for detecting a negotiation strategy used by an opponent during
the encounter. It is based on simple transforms that transform the series of offers into a series of values
determining the shape of the observed concession curve. It allows for detecting whether the partner is using a
time-dependent tactic and what is the specific tactic through determination of the beta parameter used on the
side of the negotiation partner. Such information can be further used in choosing a negotiation strategy that
can cope with a particular type of the opponent behaviour, and thus improving the negotiation outcomes.
1 INTRODUCTION
Negotiation is process of exchanging offers and
counter-offers between parties with conflicting inter-
ests that aims at finding a solution satisfying the inter-
ests of parties taking part in this interaction (Jennings
et al., 2001). There are variety of approaches of learn-
ing and reasoning during the negotiation process.
Zeng and Sycara (Zeng and Sycara, 1996) pro-
pose a learning approach based on Bayesian updat-
ing of beliefs about the environment and negotiation
partner. Li and Tesauro (Li and Tesauro, 2003) pro-
posed an approach based on approximate optimiza-
tion of expected utility using depth-limited combi-
natorial search and Bayesian updating. The work
of Hindriks and Tykhonov (Hindriks and Tykhonov,
2008) proposes to employ Bayesian learning to learn
the preference of the negotiation partner assuming
a very specific form of the preferences. However,
such approaches focus on learning the preferences’
structure but not the negotiation strategy. Oliveira
and Rocha (Oliveira and Rocha, 2000) propose a
framework for multi-issue negotiation between agents
where the bid formation is supported by reinforce-
ment learning. This approach is used for both learn-
ing from previous interaction and learning from the
current encounter.
Work by Nastase (Nastase, 2006) presents a con-
cession curve analysis which is used to predict the ne-
gotiation outcomes based on the features of the conc-
cession curve. Our approach is suitable for automated
negotiation and aims at extracting just one parame-
ter describing the shape of concession curve and its
nature is different from the nature of parameters ex-
ctracted in the work of Nastase that are suitable in the
analysis of negotiations conducted by humans.
Works such as (Oliver, 1997)(Matos et al.,
1998)(Gerding and Somefun, 2006) employ evolu-
tionary computing to determine the optimal profile
of negotiation strategies. The works by Hou (Hou,
2004) Ren and Zhang (Ren and Zhang, 2007) and the
work (Brzostowski, 2007) propose to predict the con-
cession curve using regression analysis. In this work
we propose simpler method of prediction based on
concession curve transforms which is computation-
ally very cheap. The proposed approach overcomes
the problem of wrong estimation of parameters en-
countered sometimes by regression analysis, and it
gives high level of certainty that the time-dependent
tactic is used when it is actually used.
The paper is structured as follows. In the sec-
ond section we recall the concept of decision func-
tions. The third section presents the transforms used
to transform the series of partner’s offers that is fur-
ther used to determine the parameter corresponding
to the shape of concession curve. The fourth section
presents an evaluating experiment allowing for vali-
dation of the proposed technique. The fifth section
presents conclusions.
305
Brzostowski J. and Kowalczyk R..
An Efficient Technique for Detecting Time-dependent Tactics in Agent Negotiations.
DOI: 10.5220/0003968203050309
In Proceedings of the 14th International Conference on Enterprise Information Systems (ICEIS-2012), pages 305-309
ISBN: 978-989-8565-10-5
Copyright
c
 2012 SCITEPRESS (Science and Technology Publications, Lda.)

2 DECISION FUNCTIONS
In this work we will consider the acceptance region
in a form of interval containing real numbers. Mul-
tiple attributes will be consider in further work. The
negotiation agent can use a decision function for gen-
erating offers that it is going to propose. The deci-
sion function is a function mapping a time point into
the value of offer. The time point corresponds to the
current negotiation moment. The decision function
may be dependent on different types of parameters
and values. Among them there can be negotiation
deadline, the borders of acceptance range and other
formal descriptions of agent preferences. There are
variety of ways of implementing negotiation strategy
in a form of decision function. Faratin (Faratin et al.,
1998) proposed different types of tactics which can be
used to generate negotiation behaviour. Three types
of tactics were proposed in his approach, namely: the
time-dependent tactics, the behaviour-dependent tac-
tics and resource-dependent tactics. This three types
of tactics are called pure tactics. In this work we are
only interested in the prediction of time-dependent
tactic.
The objective of an agent is to reach an agree-
ment with the negotiation partner in the time range
[0, t
max
] (t
max
- deadline). The tactic allows for gen-
eration of offer in each time point of this range. If
before proposing the offer x an agent receives from
the counterpart an offer y exceeding the value of x (in
terms of utility value) then the agent accepts y. The
time-dependent tactic is constructed in such a way
that during the whole encounter an agent will concede
up to the reservation value when it meets deadline. If
an agent a using that type of tactic wants to propose
an offer x
t
a→b
for the issue j at time t (0 ≤ t ≤ t
max
)
then that offer can be generated in the following way
(Faratin et al., 1998):
x
t
b→a
[ j] =

min
a
j
+α
a
j
(t)(max
a
j
− min
a
j
) if U
a
j
is decreasing
min
a
j
+(1 − α
a
j
(t))(max
a
j
− min
a
j
) if U
a
j
is increasing
where min
a
j
and max
a
j
are the boundaries of the ac-
ceptance range of the issue j of the agent a. The
function α
a
j
(t) is a function defined over time giving
values in the interval [0, 1] (0 ≤ α
a
j
(t) ≤ 1) that can
be further rescaled to fit the space in which the agent
is conceding. Faratin (Faratin et al., 1998) proposed
two families of functions used to implement the time-
dependent tactic, namely, polynomial and exponential
as follows:
• Polynomial: α
a
j
(t) = k
a
j
+ (1 − k
a
j
)(
min(t,t
a
max
)
t
a
max
)
1
β
• Exponential: α
a
j
(t) = e
(1−
min(t,t
a
tmax
)
t
a
max
)
β
lnk
a
j
where k
a
j
is the initial concession of agent a and β
specifies the way of conceding (shape of concession
curve).
3 TIME-DEPENDENT TACTICS
TRANSFORMS
Let us consider a function transform of the following
form:
F
1
β
( f )(x) =
Log(
f (x)− f (0)
f (t
e
)− f (0)
)
Log(x) − Log(t
e
)
(1)
where t
e
∈ (0, x). We will prove that this transform
can transform the polynomial decision function into
very simple function which is constant and equals to
β value.
Theorem 1. Let the function f be defined in the form
of polynomial decision function:
f (t) = min
a
j
+(k
a
j
+(1 −k
a
j
)(
min(t, t
a
max
)
t
a
max
)
1
β
)(max
a
j
− min
a
j
)
The transform F
1
β
transforms the function f into con-
stant function which equals
1
β
for all values of the do-
main (x ∈ [0, t
a
max
]).
Proof. f (0) = min
a
j
+k
a
j
(max
a
j
− min
a
j
)
F
1
β
( f )(x) =
Log(
(1−k
a
j
)(
min(x,t
a
max
)
t
a
max
)
1
β
)(max
a
j
− min
a
j
)
(1−k
a
j
)(
min(t
e
,t
a
max
)
t
a
max
)
1
β
)(max
a
j
− min
a
j
)
)
Log(x) − Log(t
e
)
=
=
Log(
(
min(x,t
a
max
)
t
a
max
)
1
β
)
(
min(t
e
,t
a
max
)
t
a
max
)
1
β
)
)
Log(x) − Log(t
e
)
We make a simplifying assumption that x does not
exceed t
a
max
, then:
F
1
β
( f )(x) =
1
β
Log(
x
t
e
)
Log(x) − Log(t
e
)
=
1
β
Let us now consider a transform of the following
form:
F
2
β
( f )(x) =
x∂ f (x)− f (0)
∂x
f (x) − f (0)
(2)
we will prove that this transform acts similarly to the
transform F
1
β
.
Theorem 2. Let the function f be defined in the form
of polynomial decision function:
ICEIS2012-14thInternationalConferenceonEnterpriseInformationSystems
306

f (t) = min
a
j
+(k
a
j
+(1 −k
a
j
)(
min(t, t
a
max
)
t
a
max
)
1
β
)(max
a
j
− min
a
j
)
The transform F
2
β
transforms the function f into con-
stant function which equals
1
β
for all values of the do-
main (x ∈ [0, t
a
max
]).
Proof.
F
2
β
( f )(x) =
x
∂(1−k
a
j
)(
min(x,t
a
max
)
t
a
max
)
1
β
∂x
(1 − k
a
j
)(
min(x,t
a
max
)
t
a
max
)
1
β
Let us further assume that x ∈ [0, t
a
max
] then
F
2
β
( f )(x) =
1
β
x
t
a
max
(
x
t
a
max
)
1
β
−1
(
x
t
a
max
)
1
β
=
1
β
As we have shown in the case of time-dependent
tactic there exist transforms that allow to determine
the value of β parameter when the agent is using
time-dependent tactic generated with the use of poly-
nomial decision function. However, the transforms
work for continuous functions. Therefore, we form
linearly interpolated function g(x) from the conces-
sion curve and then we transform the obtained func-
tion into functions h
1
and h
2
using two transformation
methods. In the next step we sample the transforms in
hypothetical points densly selected from the domain
of transforms. The obtained series h
1
i
and h
2
i
are aver-
aged to approxiamate the value of β and the standard
deviations for series are computed. The deviations are
used to determine the level of certainty that the poly-
nomial decision function was used by the predicted
partner.
4 EVALUATING EXPERIMENT
We run 25 negotiations for different values of β pa-
rameters for both parties using the polynomial deci-
sion function. For a fixed value of deadline (common
for both parties), aspiration levels and reservation val-
ues we run negotiations for differing values of β pa-
rameter (five possible values for both parties). We set
up the experiment in the following way: For the first
party (party a with one issue):
min
a
= 15 max
a
= 25 t
a
max
= 20
For the second party (party b with one issue):
min
b
= 10 max
a
= 20 t
b
max
= 20
As shown in the Table 1 the estimations of the value
Table 1: The values of β estimated from the view point of
the first party for the second party using the mean value of
series h
1
i
.
1
β
(a) 0.1 0.5 1 2 10
1
β
(b)
0.1 0.0986 0.0996 0.0997 0.0998 0.0998
0.5 0.4990 0.4993 0.4994 0.4995 0.4995
1 1 1 1 1 1
2 2.004 2.003 2.003 2.003 2.002
10 10.1274 10.1274 10.1274 10.1159 10.1159
Table 2: The values of standard deviations for series h
1
i
for
different negotiation scenarios analogous to the first Table.
1
β
(a) 0.1 0.5 1 2 10
1
β
(b)
0.1 0.0006 0.0005 0.0004 0.0003 0.0003
0.2 0.0014 0.0012 0.0011 0.0010 0.0009
1 0 0 0 0 0
5 0.0088 0.0086 0.0083 0.0081 0.0079
10 0.311 0.311 0.311 0.307 0.307
β parameter determined with the transform approach
are quite precise. This means that it is possible to
determine the strategy that agent b used using sim-
ple method of sequence of offers transformations.
The next Table (2) presents the standard deviations
(namely how the estimated value of β deviates from
the mean value of β over the negotiation scenario).
For all β values the standard deviations are close to
zero. Low standard deviations means that we have
high degree of confidence that the estimated values
of β are close to the actual values of β. One excep-
tion is the value of β equal to 10 where the standard
deviation is around 0.311. Therefore, the certainty
that the β value 10 was used is lower. The reason for
lower certainty in this case is the shape of concession
curve which is quite flat up to the solving negotiation
round. The Table 3 presents the estimations of β
value for the second type of transform in analogous
way as the first Table. As we can see the results are
similar; the estimations are close to the actual value of
β used by the counterpart. However, as we can see in
Table 3: The values of β estimated from the view point of
the first party for the second party using the mean value of
series h
2
i
.
1
β
(a) 0.1 0.5 1 2 10
1
β
(b)
0.1 0.0996 0.0995 0.0995 0.0996 0.0999
0.5 0.4987 0.4988 0.4989 0.4989 0.49986
1 1 1 1 1 1
2 2.0082 2.0080 2.0078 2.0073 1.9919
10 10.2397 10.2397 10.2397 9.97882 9.97882
AnEfficientTechniqueforDetectingTime-dependentTacticsinAgentNegotiations
307

Table 4: The values of standard deviations for series h
2
i
for
different negotiation scenarios analogous to the third Table.
1
β
(a) 0.1 0.5 1 2 10
1
β
(b)
0.1 0.0094 0.0054 0.0045 0.0040 0.0038
0.2 0.0152 0.01266 0.01179 0.0110 0.0107
1 0 0 0 0 0
2 0.0093 0.0906 0.880 0.0858 0.09393
10 4.6394 4.6394 4.6394 4.6499 4.6499
Table 5: The values of estimated β parameters by the use
of nonlinear regression analysis.
1
β
(a) 0.1 0.5 1 2 10
1
β
(b)
0.1 0.388 0.0297 0.0331 0.3524 0.03727
0.2 0.4987 0.4989 0.4990 0.4991 0.4992
1 1 1 1 1 1
2 2 2 2 2 2
10 10 10 10 10 10
Table 4 the standard deviations for the β value equal
to 10 are quite high (around 4.6394). Similarly, as in
the case of first transform the reason for that is the
flatness of the concession curve generated using the β
value equal to 10.
As we can see in the Table 5 the values of β es-
timated with the use of non-linear regression anal-
ysis are very precise except for small values of
1
β
.
The reason for this is that the regression algorithm
gets stucked in the local minimum while estimating
β value. That may happen for sharp values of β pa-
rameters such as 0.1 That is were the method based
on transforms outperforms the regression-based ap-
proach. Low number of data causes the regression al-
gorithm to obtain wrong estimations. As we can see in
Table 6 the values of estimated variance are very close
to 0 for all estimated values of β which means the re-
sult of regression analysis may be quite misleading
when the algorithm gets stucked in local minimum.
Such a result is obtained in the first row (when esti-
mating the value 0.1). The value of estimated vari-
ance indicates how certain we are that the polyno-
mial time-dependent tactic was used. The method
Table 6: The values of estimated variance (approximations)
obtained by the regression algorithm when estimating the
values of β.
1
β
(a) 0.1 0.5 1 2 10
1
β
(b)
0.1 0 0.000158 0.000252 0.000311 0.000377
0.2 0 0 0 0 0
1 0 0 0 0 0
2 0 0 0 0 0
10 0 0 0 0 0
based on transforms manages to estimate the value of
β quite precisely even if the certainty (standard devi-
ation) that the polynomial time-dependent tactic was
used is not very high.
5 CONCLUSIONS
We proposed a novel approach for detecting the time-
dependent tactic used by the negotiation partner. We
use simple transforms to transform the series of of-
fers into a series of values indicating what value of β
parameter is used on the side of the negotiation part-
ner. Using this method we are able to determine if the
partner is using time-dependent tactics. Moreover, we
are able to determine the β parameter used by partner.
Such an approach may be further used to choose a ne-
gotiation strategy that can cope with a particular type
of behaviour.
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