A Parallel, Multi-issue Negotiation Model
in Dynamic E-Markets
Fenghui Ren1 , Minjie Zhang1, Xudong Luo3 , and Danny Soetanto2
1
2
School of Computer Science and Software Engineering
School of Electrical, Computer and Telecom Engineering
University of Wollongong, Australia
3
School of Computer Engineering
Nanyang Technological University, Singapore
Abstract. Negotiating agents play a key role in e-markets and become more popular. However, in much existing work, the e-markets are assumed to be closed and
static, which is unrealistic. To address the issue, this paper developed negotiating agents that can adapt their negotiation strategies, outcome expectations, offer
evaluations, and counter-offers generations in dynamic, open e-markets. Also,
the proposed agents can generate multiple counter-offers according to different
preferences so as to further improve their negotiation outcomes. Finally, the experimental results show the improvements on agents’ profits by employing our
negotiation model.
1 Introduction
In recent years, electronic marketplace (e-market) has changed the traditional ways of
doing business and intelligent agents make the business processes in e-market more efficient. In an e-market, people can easily publish information, retrieve items of interest,
and negotiate with opponents concurrently. In such a frequently changing environment,
agents’ expectations on negotiation outcomes may not be achieved successfully without considering the impacts from changes of e-markets. For example, when a market
changes from a buyer’s market to a seller’s market, if buyers fail to be aware of such a
change and insist on their original expectations, the negotiation could fail due to buyers’
original expectations being hard to be satisfied in a seller’s market. To the contrary, if
sellers fail to be aware of such a change and insist on their original expectations, the
sellers may loss the chance to maximize their benefits. Therefore, in order to be successful in such highly dynamic e-market, negotiation agents should adapt their negotiation
strategies accordingly.
Many multi-issue negotiation models have been proposed. For example, the model in
[5] can achieve optimal negotiation outcomes, but it works only in the environment with
fixed number of agents. The model in [8] is also an one for multi-attribute negotiations
between two agents. However, impacts on agents’ strategies from outside options are
still not taken into account. In model of [7], a multilateral multi-issue negotiation protocol is proposed, in a cooperative scenario, by employing a mediator agent. However,
when the number of negotiation participators fluctuates, the mediator can hardly make
an unbiased and accurate response to all agents. The work in [4] studied multi-issue
D. Wang and M. Reynolds (Eds.): AI 2011, LNAI 7106, pp. 442–451, 2011.
c Springer-Verlag Berlin Heidelberg 2011
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negotiation models in incomplete information settings and illustrated equilibrium solutions for different negotiation agendas and procedures. However, their model is only
applicable in static negotiation environments. To remove the limitation, this paper will
propose a parallel, multi-issue negotiation model for open, dynamic e-markets.
The rest of this paper is organized as follows. Section 2 introduces a new model to
represent the e-markets and the negotiation issues. Section 3 proposes an offer evaluation approach. Section 4 discusses our counter-offer generation approach. Section 5
carries out experimental analysis of our model in different e-markets. Section 6 compares our work with related work. Finally, Section 7 concludes this paper.
2 E-Market and Negotiation Issue
2.1 E-Market Change and Agent’s Response
Circumstance plays a crucial role in negotiations [11]. Especially in a dynamic emarket, the market change will impact agents’ behaviours during negotiations.
Let α (α = 1 for seller, and α = −1 for buyer) denote an agent’s role, s denote the
number of sellers in an e-market, and b denote the number of buyers. Then the market’s
situation by considering the relationship between supply and demand can be defined as:
Φ(s, b, α) =
b−s
×α
b+s
(1)
Clearly, the value of Φ is in (−1, 1). Intuitively, if 0 < Φ < 1, the e-market is a
beneficial market (i.e., agents in role α have advantages in such a market); if −1 <
Φ < 0, the e-market is an inferior market (i.e., agents in role α have disadvantages); if
Φ = 0, the e-market is an equitable market (i.e., b = s and agents play fairly).
However, Formula (1) only reflects the objective status of an e-market, but does not
take agents’ subjectiveness into account. In real world markets, different people behave
differently in the same market situation. Therefore, we need a mapping from objective
market situations to subjective responses of agents. Let β denote an agent’s attitude the
market changes. In general, it can be seen that the agent has three typical attitudes when
the e-market’s situation changes, i.e., calm (β > 1), excited (1 > β > 0), and normal
(β = 1). Formally, by considering attitudes, agents’ responses to the e-market changes
are defined as:
Ψ (s, b, α, β) =
(Φ(s, b, α))β ,
if Φ(s, b, α) ≥ 0
−(−Φ(s, b, α))β , otherwise
(2)
In fact, the formula reflects well the agent’s subjective responses to e-market changes:
(1) 1 > Ψ > 0 indicates a positive response; (2) Ψ = 0 indicates a normal response;
and (3) −1 < Ψ < 0 indicates a negative response.
2.2 Issue’s Significance and Relationship
In multi-issue negotiation, the significance of each issue and the relationship between
issues play important roles for the offer evaluation, the counter-offer generation, and the
negotiation outcome [6]. Usually, the significance of issues are represented by weights,
and there are no logical relationships between issues [4]. To put into consideration the
logic relationships among the issues, here we propose alternative approach.
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Definition 1. An agent’s significance on a negotiation issue m is represented by tag
κm ∈ {N, L, I, V, E}, which means not-important (N ), little-important (L), important
(I), very-important (V ), and extremely-important (E), respectively. Γ : {N, L, I, V, E}
→ {1, 2, 3, 4, 5} maps a significance tag into its corresponding order. Atomic Preference (AP) is a collection of all issues’ significance tags i.e., AP = (κ1 , . . . , κM ), and
Complete Preferences (CP) contains all APs the agent has, i.e., CP = (AP1 , . . . , APJ ).
Definition 2. The relationship between two issues or two APs is represented by a
unique relationship tag ξ ∈ {∩, ∪}. Tag ∩ indicates a union relationship of two connected parts (i.e., an agent’s expectation on two parts connected by ∩ must be satisfied).
Tag ∪ indicates an alternative relationship of two connected parts (i.e., an agent’s expectation on only one part connected by ∪ must be satisfied).
3 Offer Evaluation
In this paper, we employ the package deal negotiation procedure [3], but do not use
multi-attribute theory [1] to evaluate offer package because (1) quantitative representation of issues’ significance does not always accord with human’s ways of thinking
[9]; and (2) The multi-attribute utility approach cannot model the logical relationship between negotiation issues. However, a human often assigns different logic relationships between their concerned issues. In this section, we propose a novel approach to perform the evaluation process in multi-issue negotiation by using significance tags and relationship tags. Let O i,t = (oi,t,1 , . . . , oi,t,M ) denote an offer package from opponent i at round t, where oi,t,m denotes opponent i’s proposal on issue m. Let O ini = (oini,1 , . . . , oini,M ) denote an agent’s initial offer package, and
γ = (γ1 , . . . , γM ) (γm ∈ {−1, 1}) indicate the agent’s preference on each negotiating issue. That is, if the agent prefers a higher value than oini,m , γm = 1, otherwise
γm = −1. Firstly, when the agent receives opponent i’s proposal oi,t,m , the proposal is
evaluated as follows:
Λ(oi,t,m , oini,m , γm ) = th
x
oi,t,m − oini,m
× γm
oini,m
+1
(3)
−x
1
where th(x) = eex −e
+e−x is the Hyperbolic Tangent function. Formula (3) (Λ ∈ (0, 2))
can model well how an agent’s initial offer is satisfied by an opponent’s proposal. For
example, suppose an agent prefers a lower value than the initial value, then γm equals
−1. When oi,t,m = oini,m , Λ = 1 and the buyer’s expectation is fully satisfied. When
oi,t,m > oini,m , 0 ≤ Λ < 1 and the buyer’s expectation is partially achieved. And when
oi,t,m < oini,m , 1 < Λ < 2 and the buyer’s expectation is overachieved. However,
formula (3) only evaluates the proposal oi,t,m based on an agent’s initial offer without
considering the market situations. To remove the limitation, we update the formula as
follows:
Θ(oi,t,m , oini,m ,γm ,s,b,α,β) =
1
Λ(oi,t,m ,oini,m ,γm )
Ψ (s, b, α, β) + 1
That is, th(0) = 0, limx→∞ th(x) = 1, and limx→−∞ th(x) = −1.
(4)
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Θ (∈ [0, 1]) can well evaluates the opponent’s proposal oi,t,m according to both the
agent’s and the market’s situations. In an equitable market, the proposal is evaluated
unbiasedly (i.e., when Ψ = 0, Θ = Λ). In a beneficial market, the proposal is undervalued (i.e., when 0 < Ψ < 1, Θ < Λ). In an inferior market, the proposal is overvalued (i.e., when −1 < Ψ < 0, Θ > Λ).
Let Θ(O i,t ) = (Θ(oi,t,1 ), . . . , Θ(oi,t,M )) indicate the evaluation results on opponent i’s all proposals. Then, these results need to be combined in order to get an overall
evaluation result on opponent i’s proposals. The traditional combination approach is the
weighted sum approach. However, we propose a non-linear combination approach by
using the significance tags, and agents’ multiple preferences are also considered. We
firstly calculate the relative importance between issues according to their significance
orders as below:
dm = Γ (κm )/
M
Γ (κm )
(5)
m=1
Then the combined evaluation result by considering all negotiation issues based on the
agent preference AP is:
AP
Tprod
(Θ(O i,t )) =
M
Θ(oi,t,m )dm
(6)
m=1
If an agent has more than one preferences, since the agent might have different significance orders on issues in different preferences, when it evaluates a proposal package,
it should consider all preferences, and select one as the final result. Different selection
criterion can be employed by agents to indicate their attitudes, i.e., a pessimistic agent
will select the minimal one; a optimistic agent will select the maximal one; while other
agents will select between these two extreme values. In this paper, we choose the maximal one as the final result. That is because a satisfaction on any one of the agent’s
preferences can lead to an agreement, and thus select the maximal one accelerate the
process to the agreement. The selection result in this paper is:
CP
Tprod
(Θ(O i,t )) =
AP
max {Tprodj (Θ(O i,t ))}
APj ∈CP
(7)
4 Counter-Offer Generation
In this section, we present a novel counter-offer generation approach by considering
issues’ significance and e-market situations. Let O m,t = (o1,t,m , . . . , oI,t,m ) denote
all offers from all available opponents on issue m at round t. In Figure 1, the x-axis
indicates opponents’ proposals on issue m, and the y-axis represents the occurrence
density of these proposals. The solid curve indicates the distribution of Om,t , and the
dotted line is the estimated distribution of O m,t+1 in the next round. The distribution of
O m,t may be different from case to case. However, without losing any generality, we
make the assumption that the shape of the distribution curve of set Om,t+1 is similar to
that of O m,t , but the range of span is changed. Suppose a buyer agent negotiates a car’s
price, then the market displayed in Figure 1 is a beneficial market for the buyer agent. In
a beneficial market, opponents’ proposals are estimated to become smaller in average
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Fig. 1. Counter-offer generation in a beneficial market for multiple issues
in the next round (i.e., Õm,t+1 < Õm,t ). The distance between the buyer’s current offer
com,t and the expected best offer ōm,t+1 in the next round is the bargain area. Then the
buyer’s new counter-offer com,t+1 is generated within this area according to the buyer’s
negotiation strategies, the remaining rounds, the distribution of O m,t , and the issue’s
significance.
Firstly, we estimate the expected best offer ōm,t+1 in the next round. Such an estimation is based on an assumption that all agents are self-interested and rational and thus
they are trying to balance their profits and negotiation success. In a beneficial market,
they will look for more profits; while in an inferior market, they will sacrifice profits in
order to increase the negotiation success. Formally, ōm,t+1 can be calculated as:
(8)
ōm,t+1 = ōm,t + γm · Ψ (s, c, α, β) · 3 D(O t )
D(O m,t ) =
I
(oi,t,m − E(O m,t ))2 · pi,m
(9)
i=1
where D(O m,t ) indicates the variance of O m,t , E(O m,t ) indicates the mathematical
of oi,t,m . We set
expectation of O m,t , and pi,m indicates the distribution probability
D(O
)
the maximal possible change of the expected
best
offer
to
3
t because 99% of
observed value locates in interval [−3 D(O t ), 3 D(O t )] in mathematics. Usually,
I
when the distribution of O m,t is a normal distribution, E(O m,t ) = I1 i=1 oi,t,m and
pi,m = 1/I.
Secondly, we modify the bargain area. As shown in Figure 1, the bargain area is originally between com,t and ōm,t+1 . However, when agents assign different significance
tags on issues, their expectations on negotiation outcomes are different. Intuitively, an
agent should concede less at more significant issues, but more at less significant issues.
In order to represent such a reality, the starting point of the bargain area needs to be
updated as follows:
com∗,t = com,t + (ōm,t+1 − com,t )(Γ (E) − Γ (κm ))/(Γ (E) − Γ (N ))
(10)
For example, if issue m’s significance tag is E, then the updated stating point equals
to the original starting point (i.e., com∗,t = com,t ), and the agent does not shrink its
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bargain area. If issue m’s significance tag is N , the updated stating point equals to the
expected best offer (i.e., com∗,t = ōm,t+1 ), and the agent minimizes its bargain area.
For issues with other significance tags, the changes of the bargain area are between
these two extreme cases. Then the counter-offer com,t+1 is generated as follows:
com,t+1 =
if t = 0
oini,m ,
com∗,t + (ōm,t+1 − com,t )( τt )λ , if t ≤ τ
(11)
Where τ is the agent’s deadline and λ is the negotiation strategy [6]. Finally, by applying
formula (11) on all issues, a counter-offer package is generated as follows.
Υ (AP, t) = (co1,t+1 , . . . , coM,t+1 )
(12)
According to Formula (10), the starting point of bargain area for issues with different
significance tag will be updated differently. If an agent has several preferences and assigns different significance on an issue in different preferences, different counter-offers
should be generated. In our proposed counter-offer generation approach, the number of
counter-offers generated by the agent in each negotiation round equals the number of
the agent’s preferences. An agent generates parallel counter-offers by considering all
preferences as follows:
Υ (CP, t) = (Υ (AP1 , t), . . . , Υ (APJ , t))T
(13)
By comparison with the traditional single counter-offer approach, the proposed approach will increase the negotiation efficiency and overall profit. Because parallel counteroffers will result an agreement quicker and decrease the lose of overall profit by considering time constraints.
5 Experiment
5.1 Experimental Settings
We set the total of agents to 100 (50 buyers and 50 sellers) and two negotiating issues
(the price and warranty of a car). For the buyer agents, their initial prices, reservation
prices, initial warranty, and reservation warranty are randomly selected between $1500
and $4500, $5000 and $15000, 5 years and 10 years, and 1.5 years and 4.5 years, respectively. For the seller agents, their initial prices, reservation prices, initial warranty,
and reservation warranty are randomly selected between $5000 and $15000, $1500 and
$4500, 1.5 years and 4.5 years, and 5 years and 10 years. For all negotiating agents, the
parameters of their negotiation strategy are randomly selected in interval [0, 2], their
negotiation deadlines are randomly selected in interval [15, 25]. For the classic negotiating agents [3], their weighting on the two issues are randomly selected in interval
[0, 1]; and for our negotiation agents, their significance tags on the issues are randomly
selected in {N, L, I, V, E}.
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(a) BAU
(b) SAU
(c) AAU
(d) ANR
(e) ANT
(f) AAN
Fig. 2. Negotiation results with the classic model
5.2 Experimental Results
To show the performance of our negotiation model, two experiments are carried out. In
the first experiment, both buyer and seller agents employ the classic negotiation model
[3] (that cannot handle the dynamics of e-markets). Both the buyer and the seller agents’
number are started from 1, and gradually increased to 50. We analyze the experimental
results, in terms of the buyers’ average utility (BAU), the sellers’ average utility (SAU),
all negotiating agents’ average utility (AAU), average negotiation rounds (ANR), average negotiation time (ANT, in millisecond), and average agreement number (AAN). In
Figure 2, the experimental results by using the classic negotiation model are displayed,
we can see that except for AAN, the other five results almost has no changes when the
number of negotiating agents changes. Both BAUs and SAUs are around 0.5 for different market situations, and AAUs are round 1.0. All negotiations are finished in-between
5 and 8 rounds, and spend around 10ms. That is because the classic negotiation model
does not consider the impacts from the e-market changes, and thus the agents cannot
adapt their behaviours when the market changes.
In the second experiment, all buyer agents employ our negotiation model, and all
seller agents employ the classic negotiation model. To simplify the experiment, we set
the buyer agents’ attitudes on market changes to normal (i.e., β = 1). The experimental
results are shown in Figure 3. It can be seen that BAUs (see Figure 3(a)) show different
values in different market situations. When it is an equitable market, BAUs are similar
as the values gained in the first experiment. However, when the market becomes more
beneficial to the buyers, BAUs increase gradually. The maximum BAU is around 1.5,
and appears when there are 50 sellers but only 1 buyer in the market. On the other
hand, when the market becomes inferior to the buyers, BAUs decreases gradually. In the
extreme case, when the market contains only 1 seller but 50 buyers, BAU is minimized
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and almost equals to 0. The reason for such differences is because the buyer agents
adapt their negotiation behaviours when the market situation changes, and try to enlarge
profits in beneficial markets, and to guarantee success in inferior markets.
Even though the seller agents cannot adapt their negotiation behaviours initiatively,
SAUs (see Figure 3(b)) are also varied in different market situations with the changes
of the buyer agents’ behaviours. In general, SAU is increased from 0 to 1 when the
market changes from an extreme buyer’s market to an extreme seller’s market. In a
buyer’s market, since the buyer agents know their advantages, they would not make
big concessions, and so the seller agents have to. By contrast, in order to beat other
competitors, the buyer agents have to make great concessions in a seller’s market, so
the seller agents’ profits are increased. However, since the seller agents employ the
classic negotiation model and cannot be aware of their advantages in a seller’s market,
they cannot further enlarge their profits subjectively as the buyer agents do in a buyer’s
market, but immediately accept offers when their initial expectations are satisfied. That
is why the maximum BAU is 1.5, but the maximum SAU is only 1.
AAUs (see Figure 3(c)) are increased around 0.2 on average by comparison with the
outcomes of classic negotiation model (see Figure 2(c)). Such an increment implies
that our negotiation model can improve the outcome of the whole market in different
market situations. In a buyer’s market, the buyer agents would like to spend more time
on bargaining to maximize their profits, and so ANRs (see Figure 3(d)) are increased in
the second experiment. However, when the buyer agents try to prevent profits loss and
to guarantee successes in a seller’s market, they would like to reach agreements as quick
as possible, and so ANRs are decreased. Nevertheless, no matter in a buyer’s market or
in a seller’s market, because the buyer agents need extra time to analyze the market
situation and accordingly select their following actions in each negotiation round, our
(a) BAU
(b) SAU
(c) AAU
(d) ANR
(e) ANT
(f) AAN
Fig. 3. Negotiation results with our model
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negotiation model could spend more time than the classic one. It can be seen that in
the most complex market (50 buyer agents and 50 seller agents), our model spends only
0.5 second more than the classic model in finishing all negotiations. However, compared
with the benefits bringed to the whole market, such a little delay is acceptable.
According to the experimental settings, since the bargain areas exist between all
buyer and seller agents, the classic negotiation model can reach agreements between all
buyer and seller agents. However, by employing our negotiation model, the buyer agents
will adapt their offer evaluation results in different market situations. Especially, in a
buyer’s market, the seller agents’ offers are usually under-valued by the buyer agents,
so the buyer agents’ requirements are not easy to be satisfied. That is the reason for the
slightly decrement on AAN in a buyer’s market (see Figure 3(e)).
6 Related Work
Dasgupta and Hashimoto proposed an approach to address the problem of dynamic
pricing in a competitive online economy where a product is differentiated by buyers
and sellers on multi-issue [2]. Agents may have incomplete knowledge of the negotiation parameters. A seller employs a collaborative filtering algorithm to determine a
temporary consumer’s purchase preferences and a dynamic pricing algorithm to determine a competitive price for the product. However, their approach pays attention only
to sellers, and our negotiation model considers both negotiation sides.
Nguyen and Jennings proposed a concurrent bilateral negotiation model to handle
multi-lateral negotiations [10]. When an agent negotiates with more than one opponents, this model treats the negotiation between the agent and each opponent as an 1-to1 negotiating thread, and a coordinator is employed to control all negotiating threads.
The coordinator will select a suitable negotiation strategy from predefined strategies for
each thread. However, their model did not consider the impacts from negotiation environment changes (i.e., the change of sellers and buyers). In contrast, our negotiation
model captures the dynamic changes of a negotiation environment.
Ren proposed a Market-Driven Agents (MDAs) model to model relationship between agents’ negotiation strategies and the negotiation environment [11]. In the MDAs
model, agents are guided by four concession factors, and these factors determine how
much concession agents can give during the negotiation based on the environment.
However, the MDAs model does not take into account the situation when the negotiation environment becomes open and dynamic, and our model address well how a
dynamic changing e-market be handled in negotiation.
By comparison with the above related work, our negotiation model has features. It
models negotiations in e-markets by considering (i) both e-markets’ and agents’ situations, (ii) both current and future possible situations of e-markets, and (iii) multiattribute and multi-preference. However, we also recognize that the performance of our
model still can be improved in aspects of time cost and negotiation success rate.
7 Conclusion and Future Work
This paper proposed a parallel, multi-issue negotiation model for dynamic e-markets.
This model describes an e-market as beneficial, inferior or normal according to the
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supply and demand. Agents evaluate offers or generate counter-offers based on the emarket situation and themselves attitudes. The experimental results showed clearly that
our negotiation model capture the e-market changes well and adapt agents’ negotiation
behaviours dynamically and accordingly. Our future work will improve the e-market
model by considering the number of goods in supply and demand relationship and opponent agents’ reputations in proposal evaluations.
Acknowledgement. The authors would like to acknowledge the financial support from
the Australian Research Council (ARC) Linkage Scheme LP0991428 and Transgrid
Australia for this project.
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