Completion of User Preference based on CP-nets in Automated
Negotiation
Jianlong Cai, Jieyu Zhan
and Yuncheng Jiang
Guangzhou Key Laboratory of Big Data and Intelligent Education, School of Computer Science,
South China Normal University, Guangzhou, China
Keywords:
CP-nets, Automated Negotiation, Preference Completion, Incomplete Information.
Abstract:
Automated negotiation is a process in which autonomous agents negotiate with the opponents to achieve
some specific purposes for their users, such as maximising the users’ benefits. CP-net is one of the most
important representations of user preferences in automated negotiation due to its ability and flexibility to
express interdependent relationship among issues. In order to be able to negotiate better on behalf of users,
a negotiating agent needs to fully understand its user’s preferences, so that it can adopt suitable negotiation
strategies and obtain ideal negotiation results. However, the preference information provided to the negotiating
agents by the users is often incomplete. Hence, based on partial preference information provided, this paper
proposes a module in negotiation framework to complete user total preferences that are represented by CP-nets.
The experimental results show the validity of CP-nets structure learning algorithm in the proposed module and
confirm that the module can help users achieve better agreements in negotiation.
1 INTRODUCTION
Negotiation is a behavioral activity for both parties
to solve problems, which is ubiquitous in human life.
With the rapid development of computer technology,
people have begun to be interested in automated nego-
tiation (Jennings et al., 2001; Kumar and Mastorakis,
2009), that is, a negotiating agent can help or repre-
sent human users to negotiate with other agents or
human opponents. Because of the characteristics of
intelligence and efficiency, negotiating agents have
begun to be widely employed in supply chain, e-
commerce and other fields (Tsimpoukis et al., 2018;
Sanchez-Anguix et al., 2021).
Modelling preferences is a necessary condition for
any step of decision analysis in the field of automated
negotiation. Therefore, different kinds of represen-
tations of user preference have been proposed in the
previous studies (Lafage and Lang, 2000; Boutilier
et al., 2004; Amor et al., 2016). However, most of the
studies ignore the situation of incomplete user prefer-
ences. In practical negotiation situations, the assump-
tion of complete user preference is often difficult to
meet due to many reasons. Firstly, users may not be
willing to spend much time to describe the utilities of
all outcomes when the issues are interdependent and
Corresponding author
the outcome space of negotiation is huge. Secondly,
perhaps due to the lack of information, users cannot
give clear preferences to all outcomes of negotiation.
Thirdly, some users may only provide partial prefer-
ence information for privacy reasons. Therefore, it is
very necessary to study how to reason and complete
user preference in negotiation scenarios with incom-
plete user preference information.
Although there are many kinds of preference rep-
resentations studied in the field of automated nego-
tiation, in this paper we focus on the one based on
Conditional preference networks (CP-nets) by consid-
ering the following advantages. Firstly, CP-nets can
represent qualitative preferences and tolerates partial
ordering, which is suitable in some scenarios where it
is difficult for the user to assess their preferences in a
quantitative form. Secondly, CP-nets allow represen-
tation of conditional preferences, which can express
interdependent relationship among issues in reality.
Finally, due to the mass of outcome space, it can be
indecisive for users to provide complete information
about their preferences of outcomes one by one, while
CP-nets provide a relatively convenient and intuitive
way to represent preferences.
This paper focuses on automated negotiation with
incomplete user preference information. The contri-
bution of this paper is twofold. Firstly, we extend au-
Cai, J., Zhan, J. and Jiang, Y.
Completion of User Preference based on CP-nets in Automated Negotiation.
DOI: 10.5220/0010909200003116
In Proceedings of the 14th International Conference on Agents and Artificial Intelligence (ICAART 2022) - Volume 1, pages 383-390
ISBN: 978-989-758-547-0; ISSN: 2184-433X
Copyright
c
2022 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
383
tomated negotiation frameworks by proposing a mod-
ule for reasoning and completing user preferences
represented by CP-nets. Secondly, we propose an al-
gorithm to learn structures of corresponding CP-nets
from partial pairwise comparisons provided by users.
The rest of the paper is organized as follows. Sec-
tion 2 reviews related work. Section 3 presents back-
ground knowledge on automated negotiation and CP-
nets. Section 4 describes the methods for user prefer-
ence modelling and completion; Section 5 discusses
the experimental setup and analyses the results. Fi-
nally, Section 6 concludes the paper with future work.
2 RELATED WORK
In this section, we will discuss related work about
both negotiations with incomplete information and
learning CP-nets. Incomplete information in auto-
mated negotiations have been studied in many differ-
ent forms, most of which focus on the uncertainty of
opponent model including preferences modelling and
strategies. Compared with opponent modelling, the
research on user modelling with incomplete informa-
tion is relatively less. (Baarslag and Gerding, 2015)
put forward a method to solve the problem of pref-
erence elicitation in negotiation. Using the idea of
greed, they proposed an optimization algorithm with
a time complexity of O(nlogn). Further than the orig-
inal algorithm, the following research (Baarslag and
Kaisers, 2017) supported the situation of stochastic
utility information. (Haddawy et al., 2003) proposed
a method for eliciting user preference models. The
method is based on the Knowledge Based Artificial
Neural Network (KBANN) pioneered by (Towell and
Shavlik, 1994). When domain knowledge is avail-
able, even in the form of weak and inaccurate hy-
potheses, much less data is required to construct an
accurate user preference model. However, the method
for user preference elicitation in (Haddawy et al.,
2003) is seen as a kind of supervised learning methods
that is not genuinely suitable for using in automated
negotiation scenarios.
The preference representation used in most auto-
mated negotiation frameworks is represented as lin-
ear additive utility functions (Baarslag, 2016), which
is simple and intuitive to compute. However, in prac-
tical situations, there is likely to be interdependence
among the issues of negotiation. CP-nets allow rep-
resentation of conditional preferences, which is more
intuitive to be used to indicate preferences (Boutilier
et al., 2004). Since CP-net represents a partial order
over outcome space, learning CP-nets can be seen as
a ranking learning of preferences from known pair-
wise comparisons (Liu et al., 2018). (Goldsmith et al.,
2008) investigated the computational complexity of
testing dominance and consistency in CP-nets, and
proved that complexity of testing dominance and or-
dering queries are in general NP-hard. CP-nets can
be cyclic or acyclic, but for the sake of intuition
and consistency, the CP-nets we describe default to
acyclic CP-nets. (Liu et al., 2018) learn structure of
CP-nets by calculating dependent degree among at-
tributes. However, most studies of structure learning
only focus on binary-valued CP-nets, which is limited
in the field of automated negotiation.
(Dimopoulos et al., 2009) proposed an algorithm
that converts pairwise comparisons to binary-clauses
to learn structure of CP-nets. For employing it in
automated negotiation scenarios, we have extended
the algorithm by three aspects that will be described
in detail in Section 4. (Aydo
˘
gan and Yolum, 2010)
first apply CP-nets as preference representations to
utility-based automated negotiation, and extend the
algorithms in (Aydo
˘
gan et al., 2015). However, this
is an estimate of the utility of preferences only if the
CP-nets is known, while our work focuses on learning
unknown CP-nets in automated negotiation scenarios.
3 PRELIMINARIES
In this section, we give a brief overview of the ba-
sic knowledge. We adopt a basic bilateral multi-
issue negotiation scenarios, which has been widely
used in the field of negotiation. V = {X
1
,...,X
n
}
is the set of issues in negotiation domain. Each
issue X
i
is associated with a domain of values
DOM(X
i
) = {x
i1
,...,x
im
}. The negotiation domain
= DOM(X
1
) × · · · × DOM(X
n
) is the set of all pos-
sible negotiation outcomes o. o[X ] denotes the assign-
ment of issue X. The goal of negotiation is to reach an
agreement which is an acceptable outcome for all par-
ties. We denote the set of all assignments to X V
by Asst(X ). For example, we set C = {C
1
,C
2
}, then
Asst(C ) = Dom(C
1
) × Dom(C
2
). For the decision
maker, preference relationship follows a strict partial
order, which is indicated by the symbol . If one
prefers o
2
to o
1
, then it can be denoted by o
1
o
2
.
Next, we introduce the concepts of CP-nets and
preference graph (Boutilier et al., 2004).
Definition 1 (CP-nets). A CP-net is a directed acyclic
graph (DAG) model G, in which nodes represent is-
sues and edges represent the dependencies between
issues. If there is a directed edge from issue X
j
to
issue X
i
, then the preference of X
i
involves X
j
for the
user, which is denoted by Pare(X
i
) = {X
j
}. Each issue
X
i
V holds a condition preference table CPT (X
i
),
ICAART 2022 - 14th International Conference on Agents and Artificial Intelligence
384
Figure 1: A sample CP-net for travel domain with issues
location(L), season(S), duration(D).
which represents the preference ordering of assign-
ments of X for different assignments of Pare(X
i
) in the
G. If X
i
V , DOM(X
i
) is binary, it is called binary-
valued CP-net. If not, i.e., X
i
V , the amount of
possible assignments of DOM(X
i
) is more than 2, it is
called multi-valued CP-net.
The following is an example for a CP-net.
Example 1 (Travel Domain). Figure 1 illustrates a
CP-net that shows Justin’s preferences to travel with
three issues: Location, Season and Duration. In this
example, l
1
denotes Paris and l
2
denotes Hawaii; s
1
denotes Winter and s
2
denotes Summer; d
1
denotes
3days and d
2
denotes 7days. When Justin makes a
choice about the duration of the travel, the prefer-
ence for 3days and 7days is conditional. If Paris
and Winter are selected or Hawaii and Summer are
selected, he prefers 7days to 3days; If Paris and
Summer are selected or Hawaii and Winter are se-
lected, he prefers 3days; Note that, comparing the
preference of two outcomes, ancestral values domi-
nate over descendant values. In this example, no mat-
ter D takes d
1
or d
2
, all outcomes selecting l
2
and s
2
have priority over outcomes selecting l
1
and s
1
.
Definition 2 (Preference Graph.). Preference graph
is a DAG induced from the CP-net G. Nodes in pref-
erence graph stand for all outcomes in a negotiation
domain, in which the root node presents the worst out-
come for the user and the best outcome placed at the
leaf node. Each directed edge represents an improv-
ing flip. By transitivity, if there exists a path in a pref-
erence graph from o
i
to o
j
, then o
i
and o
j
are com-
parable, and o
i
o
j
, otherwise o
i
and o
j
are non-
comparable or called indifferent.
Figure 2 is a preference graph of the CP-net de-
scribed in Example 1. An edge from o
1
= l
1
s
1
d
1
to o
2
= l
1
s
1
d
2
in this preference graph denotes an
improving flip on DOM(D), meaning that the user
prefers o
2
to o
1
(o
1
[D] = d
1
and o
2
[D] = d
2
).
We will introduce the definition of preference
database, which will be used in our algorithms.
Figure 2: Preference graph induced from Figure 1.
Definition 3 (Preference Database). Given two out-
comes o and o
0
in a CP-net G, if o and o
0
are compa-
rable, they make up a comparable pairwise compari-
son stored in the preference database P . If o o
0
, it
denotes (o,o
0
), otherwise, it denotes (o
0
,o). When all
comparable pairwise comparisons derived from the
preference graph which is induced from given CP-
net are in the preference database, we call it stan-
dard preference database. When the set of compa-
rable pairwise comparisons derived from the CP-net
learned by given preference database, we call that
learned preference database.
In this section, we outlined the basics required for
this paper. In the next section, we will introduce the
module we propose and algorithms used in this paper.
4 USER MODELLING
4.1 Module for Preference Completion
Figure 3: The automated negotiation framework with mod-
ule for completion of user preference.
Due to the incomplete information, the agent
needs to estimate the user preference model before
conducting automated negotiation. We propose a
module to complete this task shown in Figure 3. Since
we assume that users preferences are represented by
CP-nets, the first thing we address is structure learn-
ing of CP-nets. The structure of CP-net is learned
from a set of pairwise comparisons provided from the
user, and then the preference graph is induced from
Completion of User Preference based on CP-nets in Automated Negotiation
385
the learned structure. There may be some offers that
are not comparable based on the preference graph.
However, most negotiation strategies and opponent
modelings are based on quantitative preferences lead-
ing to a totally ordered set of outcomes. Therefore,
we use the appropriate heuristics method (Aydo
˘
gan
et al., 2015) to transform qualitative preferences into
quantitative preferences.
4.2 Structure Learning of CP-nets
Algorithm 1: learn(Issue set V , preference database P ).
Output: a learned CP-net G with respect to P
1: G
/
0;R
/
0;X V ; k 0
2: Add all issues in V with empty CPT into G.
3: while k < |V | do
4: if k = 0 then
5: R findRoots(P,X , G)
6: X X \ R
7: else
8: added extendNetwork(P ,X ,V , k,G)
9: X X \ added
10: end if
11: if X =
/
0 then
12: return G
13: end if
14: end while
15: if X 6=
/
0 then
16: learningWithMaxSAT(P , X ,R ,G)
17: end if
18: return G
We present an algorithm to tackle the problem of
structure learning, which extends the algorithm pro-
posed by (Dimopoulos et al., 2009) to better accom-
modate automated negotiation scenarios. As shown in
Algorithm 1, main procedure learn() takes a prefer-
ence database P provided from user and the issue set
V as input, and outputs an acyclic CP-net that satis-
fies the standard preference database as much as pos-
sible. At first, the algorithm maintains an empty CP-
net G and a set X containing issues to be learned, k
denotes the number of provisional parents of issue X,
where the process loops until either k = |V | or the CP-
net G is constructed. Since the assignment of ances-
tor nodes (issues) impact the preferences of descen-
dant issues, accurate derivation of the root issues in
CP-nets is crucial. However, the original algorithm is
essentially an approximate learning algorithm, which
is not accurate enough. For the above reasons, first
we extend the original algorithm as follows.
When k = 0, we call Algorithm 2 f indRoots() to
find root issues in the CP-nets. Considering every X
in X , X will be a root issue if there exists an ordering
Algorithm 2: f indRoots(P ,X , G).
Output: issue set R
1: R
/
0
2: for X in X do
3: I X \ X
4: if exist an ordering of values of X that satis-
fies Comparisons = {P | o[I ] = o
0
[I ] } then
5: R .add(X)
6: createCPT (X,ordering)
7: end if
8: end for
9: return R
Algorithm 3: extendNetwork(P , X , V ,k,G).
Output: issue set added
1: added
/
0
2: for X in X do
3: U provisionalParentSet(X,X ,G)
4: K parentCombinations(U,k)
5: for K in K do
6: I X \ (X K)
7: parentOrNot(K,X,I )
8: end for
9: if One of K K is the parent of X then
10: added.add(X)
11: end if
12: end for
13: return added
of values of X that satisfies comparisons set {P |
o[I ] = o
0
[I ]}, where I represents a subset of X except
X. That is, the preference ordering of X is not condi-
tioned by any assignments of the other issues. Finally
it creates the CPT (X) based on ordering. Once the
CPT (X) is created, X will be removed from the set
X .
When k > 0, we call extendNetwork() shown in
Algorithm 3, traversing X in the set X to extend
the G by completing CPT (X). During the travers-
ing, provisionalParentSet() returns a provisional par-
ent set of X, denoted by U, which guarantees that
the learned CP-net is acyclic. parentCombinations()
returns a set K of combinations of k elements se-
lected from U. During iterating through K in K ,
parentOrNot() decides whether K can be the par-
ent combination of X in G. parentOrNot() exam-
ines pairwise comparisons (k
i
x
i
i
i
,k
j
x
j
i
j
) P , where
k
i
,k
j
Asst(K ), x
i
6= x
j
, x
i
,x
j
Asst(X), i
i
= i
j
,
i
i
,i
j
Asst(I), and chooses the suitable clauses in
k
i
: x
i
x
j
and k
j
: x
i
x
j
leading to no contradic-
tion among all clauses selected. Taking an example of
contradiction, a
i
: b
i
b
j
, a
i
: b
j
b
k
and a
i
: b
k
b
i
have been selected, then the CPT (B) is induced as
ICAART 2022 - 14th International Conference on Agents and Artificial Intelligence
386
a
i
: b
i
b
j
b
k
b
i
. The above problem can be
converted into Boolean satisfiability problem (SAT).
Since the number of clauses in the element of the set
are no more than 2, the SAT instance above is the 2-
SAT, which could be solved in polynomial time. In
this paper, we employ solvers (Morgado et al., 2014;
S
¨
orensson and Een, 2005) for solving SAT. Each unit
can be separated into two parts to be encoded, one
is the assignment of K, and the other one is the re-
lationship between assignment of X . As an example,
a
1
: b
1
b
2
can be encoded as α
1
, a
1
: b
2
b
1
can be
encoded as ¬α
1
, and a
2
: b
1
b
2
is encoded as β
1
. Fi-
nally, it solved the 2-SAT and writes into the CPT (X)
with the decoded results. We take an example for de-
scribing this process.
Example 2. Consider the issues A, B, C with values
{a
1
,a
2
}, {b
1
,b
2
,b
3
}, {c
1
,c
2
} respectively. During
the invocation of parentOrNot({A},B, {C}) (deter-
mine whether {A} is the parent of B with the same
assignments of {C}), given pairwise comparisons are
as follow:
(1) a
1
b
1
c
1
a
1
b
2
c
1
, (2) a
2
b
1
c
2
a
1
b
2
c
2
,
(3) a
1
b
2
c
1
a
1
b
3
c
1
, (4) a
2
b
2
c
1
a
1
b
1
c
1
,
(5) a
1
b
1
c
2
a
1
b
3
c
2
, (6) a
1
b
3
c
1
a
2
b
1
c
1
.
Deduce these pairwise comparisons above:
(1) a
1
: b
1
b
2
, (2) a
2
: b
1
b
2
or a
1
: b
1
b
2
,
(3) a
1
: b
2
b
3
, (4) a
2
: b
2
b
1
or a
1
: b
2
b
1
,
(5) a
1
: b
1
b
3
, (6) a
1
: b
3
b
1
or a
2
: b
3
b
1
.
We associate the elements of {A} with component of
Boolean variables as follows: the assignment a
1
α,
a
2
β. And the relationship b
i
b
j
are associated
with subscript. Based on the above rules, the result-
ing SAT instance is (α
1
) (β
1
α
1
) (α
2
) (¬β
1
¬α
1
) (α
3
) (¬α
3
¬β
3
). And the solution of SAT
instance above are (α
1
,α
2
,α
3
,¬β
1
,¬β
3
). Consider-
ing first three elements (α
1
,α
2
,α
3
), they can be de-
coded as a
1
: b
1
b
2
, a
1
: b
2
b
3
and a
1
: b
1
b
3
respectively, which can be deduced an ordering
a
1
: b
1
b
2
b
3
and written into the CPT (B) with
a
1
: b
1
b
2
b
3
. The remaining only have 2 clauses
a
2
: b
2
b
1
, a
2
: b
3
b
2
. According to transferability,
it could still deduce a
2
: b
3
b
2
b
1
. Therefore, {A}
is the set of parent of B, and CPT (B) is created.
The second extension is described as follows:
Firstly, there may be such a situation that more than
one K satisfies being the parent of X , while only one
K can be parent of X , in principle. To cope with this
situation, we consider the count of clauses, K with
maximum count of clauses will be the parent of X.
Secondly, once the ordering is incomplete, it is neces-
sary to make a completion. Therefore, We use the
method BordaCount (Emerson, 2013) to determine
the incomplete position in the ordering.
Algorithm 4: learningWithMaxSAT(P ,X , R , G).
1: for X in X do
2: for R in R do
3: f it = Fitness(X,R)
4: end for
5: R
i
= argmax( f it)
6: R
i
is a parent of X, and create CPT (X)
7: end for
8: return
The following is the third extension of the original
algorithm. Back to the main procedure, if there are is-
sues remaining in the set X after completion of the
traversal on K, original algorithm will return False
to indicate failure of learning, which is not available
for automated negotiation scenarios. Therefore, we
calls learningWithMaxSAT () shown in Algorithm 4
to learning remaining issues. This function is sim-
ilar to the extendNetwork() shown in Algorithm 3.
For less complexity, the parents of remaining issues
X X is considered from R , and only one issue could
be the parent of X. The method that decides whether
R R can be the parent of X translates the prob-
lem into a SAT instance. But we only need to solve
for its maximum satisfiable (Max-Sat) solution. We
choose the one with the maximum satisfaction rate
as the parent of X and create CPT (X ). When all
CPT (X), X V have been created, the CP-net G is
completed and main procedure learn() returns G.
4.3 Transformation of User Preferences
Given a CP-net, the ordering of the relationships
among the outcomes is a partial order sequence, so
there will be non-comparable pairwise comparisons
in most of the time. In order to better use various
strategies in automated negotiation scenarios, trans-
forming qualitative preferences into quantitative pref-
erences is useful that agent can get a total ordering
of outcomes and know all utility of outcomes in that
domain. The method Taxonomic Heuristic (TH) pro-
posed by (Aydo
˘
gan et al., 2015) is used to handle this
problem. We briefly summarized below. Considering
a preference graph induced from a given CP-net, the
root node keeps the worst outcome and the leaf node
keeps the best outcome for the user. That is, given
two outcomes, the dominance between them is deter-
mined by their depth (length of the longest path from
the root node to this node). The higher depth one is
assigned by higher utility.
U(o
i
) = Max(U(Parent(o
i
))) + ran (1)
According to Equation (1) , the outcome’s utility is
equals the maximum utility among its parents plus
Completion of User Preference based on CP-nets in Automated Negotiation
387
a random value ran (0, 1], which ensures its util-
ity is higher than its ancestors’ and maximize leaf
node’s teutility as well. Although the randomized
approach results in an unstable ordering among non-
comparable pairwise comparisons, it provides a ref-
erence to user for non-comparable pairwise compar-
isons, and comparable pairwise comparisons are not
affected. Hence, the overall impact is not significant.
5 EXPERIMENTS
In order to demonstrate the effectiveness of our mod-
ule, the experiments were divided into two parts: one
is to evaluate the performance of structure learning
and the other is to demonstrate the feasibility of our
module in negotiation scenarios.
5.1 Performance of Structure Learning
To evaluate the performance of structure learning, we
consider experiments of learning CP-nets with 7 is-
sues. We consider 300 randomly generated CP-nets
with the number of edges from 1 to 10, where each as-
signment of edges randomly generates 30 CP-nets and
we ensure all CP-nets are acyclic and multi-valued.
To test learning performance with 20% of standard
database (including noise data), the metrics we se-
lected are the similarity of structure, error and accu-
racy of learning root issues. The formula of similarity
of structure is defined as follows:
Similarity =
|V |
n=1
sim(X
i
), (2)
where
sim(X
i
) =
score(X
i
) if X
i
is root issue,
r
p
/(e
p
+ r
p
)
|V |
otherwise,
(3)
score(X
i
) =
1
|V |
if X
i
0
is root issue,
0 otherwise.
(4)
In Equation (3), X
i
and X
0
i
denote an issue in learned
CP-net and original CP-net, respectively. r
p
denotes
the number of parent of X
i
learned accurately and e
p
denotes the number of parent of X
i
learned by error.
When Similarity = 1, it means the learned structure
is exactly the same as the given structure. The error
is the difference between learned preference database
and standard preference database. Equation (5) de-
scribes the formula for calculating error:
error =
num(incorrect pairwise comparisons)
num(standard preference database)
. (5)
Figure 4: This results of learning CP-nets in different edges.
num(incorrect pairwise comparisons) includes the
pairwise comparisons that are in standard prefer-
ence database but not in learned preference database
and are contrary to the facts by standard preference
database.
The experiment results of structure learning are
shown in Figure 4. The horizontal coordinate indi-
cates the edge number in a CP-net. Considering the
dominance of the CP-nets, the performance of learn-
ing the root issues accurately may be more important
than that of learning other issues in negotiation. The
blue line denotes the probability of accurately learn-
ing all root issues in the experiment. As we expected,
the performance of learning decreases with increasing
structural complexity. Results show that the structure
of the CP-net can be roughly learned with given data.
5.2 Application in Negotiation Scenario
To demonstrate the effectiveness of our framework,
we applied our module to automated negotiation sce-
narios and tested its performance. We randomly gen-
erated five domains with five issues for experiment.
The preference profiles are generated with CP-nets
model for two dummy users by given domains, but
the agents just know 20% of standard preference
database. Each domain is used for ten epochs of ne-
gotiation. For fairness, the agents will hold prefer-
ence profile of counterpart to compete repeat, i.e., two
times of negotiation per epoch. We investigate three
test cases. In each case, two agents (A and B) with
the same bidding strategy compete with each other.
There are three subcases in each case. In the subcase
1, both agents use our module (denote as our.vs.our.).
In the subcase 2, agent A uses our module while agent
B does not. In the subcase 3, both two agents estimate
user model randomly. The classic time dependent tac-
tics proposed by (Faratin et al., 1998) are used for
each case. Its curve of utility thread and equation are
shown in Figure 5.
The utility threshold varies over time. When
β < 0, it adopts an aggressive static called Boulware;
When β = 0, the function curve is a straight line and
the static is called Linear; When β > 0, the agent
ICAART 2022 - 14th International Conference on Agents and Artificial Intelligence
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Figure 5: The curve of utility thread.
Table 1: The results of negotiation in the case Boulware.
Boulware
uti.A uti.B round soc.
Dom.1
our. vs. our. 0.46 0.48 451.20 0.94
our. vs. bas. 0.61 0.41 358.35 1.02
bas. vs. bas. 0.43 0.46 261.50 0.88
Dom.2
our. vs. our. 0.57 0.61 521.70 1.18
our. vs. bas. 0.82 0.64 395.40 1.45
bas. vs. bas. 0.50 0.56 342.90 1.05
Dom.3
our. vs. our. 0.62 0.61 509.90 1.23
our. vs. bas. 0.76 0.34 368.60 1.10
bas. vs. bas. 0.38 0.51 301.60 0.89
Dom.4
our. vs. our. 0.62 0.60 419.15 1.22
our. vs. bas. 0.78 0.33 396.35 1.11
bas. vs. bas. 0.51 0.42 272.00 0.93
Dom.5
our. vs. our. 0.68 0.66 276.35 1.35
our. vs. bas. 0.73 0.60 372.75 1.34
bas. vs. bas. 0.43 0.45 302.85 0.88
with this static called Conceder will make conces-
sions quickly. Each negotiation is limited to 1000
rounds, i.e., t
max
= 1000. The range of utility of
each outcome is normalized at [0,1], i.e., u
min
= 0
and u
max
= 1. The protocol used in this simulation
experiments is alternating-offers protocol. Both sides
take turns to alternate bids until time runs out or one
of agent offers to terminate the negotiation. If one of
agent offers to accept opponent’s offer, the agreement
is reached with the last bid offered.
The results of average utility, average round and
average social welfare with β = 0.5, β = 1 and β = 2
are shown in Table 1, Table 2 and Table 3, respec-
tively. It is intuitive that in any subcase, the use of
Conceder results in the minimum rounds per nego-
tiation. The results of subcase 2 in all cases show
that the average utility obtained by agent A is always
higher than that obtained by agent B, which verifies
the effectiveness of our model for user modelling. By
comparing results in subcase 1 and subcase 3, average
social welfare obtained by agents in subcase 1 is more
than that in subcase 3. The negotiation in subcase 1
takes more time (average round) than that in subcase
3. Combining two analyses above, higher social wel-
Table 2: The results of negotiation in the case Conceder.
Conceder
uti.A uti.B round soc.
Dom.1
our. vs. our. 0.46 0.48 46.95 0.94
our. vs. bas. 0.57 0.38 39.25 0.94
bas. vs. bas. 0.42 0.44 9.85 0.86
Dom.2
our. vs. our. 0.58 0.63 73.70 1.21
our. vs. bas. 0.69 0.57 41.35 1.25
bas. vs. bas. 0.47 0.48 16.90 0.94
Dom.3
our. vs. our. 0.64 0.56 59.85 1.21
our. vs. bas. 0.75 0.31 26.95 1.06
bas. vs. bas. 0.46 0.40 9.50 0.85
Dom.4
our. vs. our. 0.61 0.61 30.35 1.21
our. vs. bas. 0.71 0.43 29.80 1.14
bas. vs. bas. 0.46 0.55 12.30 1.01
Dom.5
our. vs. our. 0.67 0.67 11.75 1.34
our. vs. bas. 0.70 0.59 33.25 1.28
bas. vs. bas. 0.47 0.48 12.05 0.95
Table 3: The results of negotiation in the case Linear.
Linear
uti.A uti.B round soc.
Dom.1
our. vs. our. 0.49 0.51 218.40 1.00
our. vs. bas. 0.58 0.42 369.45 1.00
bas. vs. bas. 0.44 0.49 76.10 0.93
Dom.2
our. vs. our. 0.64 0.64 266.95 1.28
our. vs. bas. 0.77 0.61 380.45 1.37
bas. vs. bas. 0.43 0.48 103.05 0.91
Dom.3
our. vs. our. 0.59 0.63 258.50 1.22
our. vs. bas. 0.73 0.35 404.95 1.08
bas. vs. bas. 0.43 0.42 73.05 0.85
Dom.4
our. vs. our. 0.58 0.62 168.00 1.20
our. vs. bas. 0.75 0.38 401.90 1.13
bas. vs. bas. 0.45 0.59 77.85 1.04
Dom.5
our. vs. our. 0.66 0.68 96.95 1.34
our. vs. bas. 0.72 0.62 360.00 1.34
bas. vs. bas. 0.45 0.49 102.35 0.95
fare was obtained despite the decline in utility thresh-
olds with the passage of time, which reflects that
agents with our model are willing to spend more time
on negotiation with opponent towards higher utility.
6 CONCLUSION
This paper studied how to complete user preference
with incomplete information in automated negotiation
scenarios where user preferences are represented by
CP-nets. Firstly, we extended the method of learn-
ing CP-nets (Dimopoulos et al., 2009) to reveal the
dependencies among issues, in which the extensions
including (1) special handling of the root issues to
learn more accurately; (2) optimising the choice of
provisional parents during learning structure; and (3)
avoiding failing to learn CP-nets. Secondly, we esti-
mate utility of offers by TH after completion of CP-
nets, making the preference representations of CP-
nets can be applied in automated negotiation. Finally,
we experimentally demonstrated the feasibility of our
module for completion of user preference in negoti-
ation. Much more could be done in the future. For
Completion of User Preference based on CP-nets in Automated Negotiation
389
example, due to the structures of CP-nets are inter-
pretative, users can easily express their attitude to-
wards the effect of preference completion, then how
to make agents interact with users efficiently to im-
prove the accuracy of completion of preference is one
of the most important problems should be address in
the future.
ACKNOWLEDGEMENTS
The works described in this paper are supported by
the National Natural Science Foundation of China un-
der Grant Nos. 62006085, 61772210 and U1911201;
Guangdong Province Universities Pearl River Scholar
Funded Scheme (2018); Project of Science and Tech-
nology in Guangzhou in China under Grant Nos.
202007040006 and 202102020948; Natural Science
Foundation of Guangdong Province in China under
Grant No. 2018A030310529; Project of Department
of Education of Guangdong Province in China under
Grant No. 2017KQNCX048.
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