Decision Support Systems 60 (2014) 55–67
Contents lists available at ScienceDirect
Decision Support Systems
journal homepage: www.elsevier.com/locate/dss
A single issue negotiation model for agents bargaining in dynamic
electronic markets
Fenghui Ren ⁎, Minjie Zhang
School of Computer Science and Software Engineering, University of Wollongong, Australia
a r t i c l e
i n f o
Available online 5 June 2013
Keywords:
Agent negotiation
Agent bargain
Electronic marketplace
Dynamic negotiation environment
a b s t r a c t
Electronic Commerce has been a significant commercial phenomenon in recent years, and brings more benefits to people by comparison with the traditional market in aspects of cost, convenience and efficiency. The use
of agent technology in e-markets for automatic bargains between buyers and sellers further increases the advantages of the e-market. However, most of existing agent-based bargain strategies assume a fixed number of
negotiation participants, which may fail to enlarge agents' profits or to lead a bargain to a success when these
strategies are applied in the e-market-based agent negotiations straightway. Problems such as unexpected
changes on negotiation participants, possible changes on agents' expected negotiation outcomes, and unexpected switching in-between the buyer's and seller's markets need to be considered in order to guarantee
agents' benefits and the success of negotiations. This paper proposes a novel agent negotiation model to
help agents to perform a more effective bargain in e-markets by considering the objectiveness of the
e-markets and the subjectiveness of the agents. The e-market situation by considering the number of bargain
participants is proposed to reflect the objectiveness of the e-markets, and the agents' negotiation attitudes is
introduced to indicate agents' responses to possible changes of the e-markets. Both the objectiveness of
e-markets and the subjectiveness of agents are taken into account in negotiation procedures such as offer evaluation, negotiation decision making and counter-offer generation. Experimental results on a simulated
e-market illustrate the benefits and efficiency of the proposed negotiation model in handling agents bargain
problem in complex and dynamic e-market environments.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Electronic market (e-market) has changed significantly the traditional way of doing business in recent years and has become a very
important commercial phenomenon [2]. By comparing with the traditional marketplaces, the benefits of e-market are the lower operation
cost and higher efficiency. By trading through an e-market, merchants
can save their budgets on business maintenance by avoiding physical
shops and shop assistants. Also, shoppers do not need to visit shops in
person which can save costs on traffic and time. The e-market is also
more efficient in reaching deals than the traditional marketplace. That
is because all participants of an e-market can collect information
about their concerned items and communicate with potential trading
partners in a timely manner. Furthermore, the usage of autonomous
agents in e-market trading makes the e-market more efficient [24,29].
By employing autonomous agents, participants of an e-market do
not need to perform the repeated work, such as the information retrieval and the price bargaining, but just let the agents know of
their preferences and expectations during a trading [20,22]. Then the
agents can perform the automatic item searching and price bargaining
with the potential trading partners, and reach a reasonable agreement
⁎ Corresponding author.
E-mail addresses: fren@uow.edu.au (F. Ren), minjie@uow.edu.au (M. Zhang).
0167-9236/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.dss.2013.05.020
according to the participants' expectations. Usually, the agent negotiation is employed by agents for bargaining.
Agent negotiation has been an important research topic in agent and
multi-agent systems for many years. The literature indicates achievements from researchers. Faratin et al. [7,28] proposed a well-known negotiation decision function by considering time constraints and defined a
number of strategies and tactics for different negotiation purposes in service oriented applications. Lai et al. [17,18] employed a third party, i.e., a
non-biased mediator, into agent negotiation to help agents to solve the
decision making problem caused by incomplete information on negotiation opponents, so as to lead the negotiation to the Pareto optimality.
Fatima et al. [8–10] also studied negotiation models in incomplete information settings in different negotiation scenarios and illustrated equilibrium solutions in different negotiation agendas and procedures.
Besides the above works on static negotiation environments, some
works on dynamic negotiation environments have also been developed. Fatima et al. [11] proposed several negotiation strategies to
help agents to achieve approximately optimal outcomes in dynamic
negotiation environments through improving computational efficiency and a little bit of loss in negotiation equilibrium. Mason et al. [21]
proposed price prediction strategies to help agents to estimate possible changes in markets, and the consequences of these changes. The
authors demonstrated that the proposed prediction strategies can
help agents to improve their profits in dynamic markets. Kurbel et al.
56
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
[16] introduced a model with fuzzy constraints on an e-job market. A
negotiation protocol and several negotiation strategies were proposed
to address the challenges of multiple party negotiations in complex
e-markets. Furthermore, Li et al. [19] proposed a confidence-based negotiation model for negotiations in complex environments. Agents
would keep the confidence information about the negotiation opponents, and apply different strategies and/or procedures in negotiating
with opponents in different confidence levels.
Although the above related works have reached great achievements in agent negotiation, challenges of e-market negotiation still
exist. For example, most of existing agent negotiation models require
agents to predefine reservation offers on negotiation outcomes before
negotiations start, and agents' actions during a negotiation are decided mostly by the reservation offers [4]. However, according to our
studies on several models of e-markets [5,6,23], and the real world
e-markets, it is noticed that in an open and dynamic e-market,
changes of a market situation such as the number of sellers and buyers
may impact agents' expectations on negotiation outcomes. In a dynamic e-market, agents do not necessarily need to fix their reservation
offers throughout a negotiation, but may modify them during a negotiation dynamically when the e-market situation changes. We further
noticed that if agents fix reservation offers in dynamic e-markets, their
profits might be damaged. The reasons are: (1) agents may have no
clear idea about e-market situations before a negotiation, and the reservation offer is usually given by agents without considering the
e-market situations; and (2) the evaluation results based on the
fixed reservation offers may fail in indicating an item's real value in
different market situations. For example, if an inexperienced house
purchaser predefines his/her reservation offer without careful investigation of the real-estate market, it may lead the purchaser to two possible disadvantageous outcomes, i.e., (i) the house purchaser may
undervalue properties' values in the market and not accept any price
higher than the reservation offer, so the potential purchaser may not
find any satisfied property in the market and negotiations between
all property sellers might fail; and (ii) the house purchaser may overvalue properties' values in the market. Even though the purchaser can
finally find a property in the market, his/her profit will be damaged as
well. In order to solve such an issue in dynamic e-markets by considering the relationship between demand and supply, we propose a
negotiation model in this paper to dynamically modify agents' negotiation behaviors based on changes of the number of an e-market's
participants and agent's motivation on accomplishment of a negotiation.
The work presented in this paper is based on our previous work in [25].
In this paper, we extend the modeling approach of an e-market to provide
a better offer evaluation function and counter-offer generation function in
an open and dynamic e-market. Also, we extend the experiment from five
agents to fifty agents, and provide much more explanations on the experimental results.
The rest of this paper is organized as follows. Section 2 introduces
the proposed negotiation model, which includes an offer evaluation approach, a counter-offer generation approach and a negotiation protocol.
Section 3 illustrates experimental results of the proposed model in different market situations. Section 4 compares the proposed model with
some related works, and Section 5 concludes the paper and introduces
our future work.
2.1. Principle
Through our studies, we notice that in the real world, although
people can predefine reservation offers in advance, in most cases it is
not necessary for them to insist on their reservation offers throughout
the negotiation [27]. For example, in a dynamic market, a hesitant
buyer may look forward to gain more benefit when he/she notices
that his/her original expectation can be satisfied easily by most sellers.
On the other hand, a ‘rushing’ buyer may accept an offer even if the
offer is worse than his/her reservation offers. However, most existing
agent negotiation models do not take these situations into account.
The motivation of this research is to introduce a sophisticated negotiation model to advice agents how to modify their negotiation behaviors in open and dynamic negotiation environments.
In our proposed negotiation model, agents do not need to
predefine their expectations on negotiation outcomes as the reservation offers, because agents' expectations may be changed when the
market situation changes. Contrary to that, agents express their eagerness to complete the negotiations as a desire (∈[0,1]), and use
the desire to make negotiation decisions. The higher the desire, the
more eager the agent wants to complete the negotiation. In comparison with the reservation offer, the desire reflects an agent's eagerness to complete a negotiation and has the following advantages:
(1) agents' desires are independent on the e-market situations, but
the reservation offer selection needs to consider the e-market situations. Therefore, the desire is more suitable for a dynamic e-market;
(2) it is more practical for agents to predefine a desire to express
their eagerness to complete a negotiation than to predefine an
expected benefit when the benefit could be greatly impacted by the
dynamics of an e-market; and (3) the negotiation process in an
e-market is usually completed in a short time, and the agents almost
have no time to update their expectations on negotiation outcome
manually, the use of desire can solve this problem because agents'
eagerness to complete a negotiation can easily be decided by agents
in advance and do not change during the negotiation.
In general, an urgent agent will have a high desire to complete a
negotiation, but a hesitant agent will have a low desire to complete
a negotiation. During the negotiation, when the e-market situation
changes, the actual evaluation on the opponent's offer and the
counter-offer generation are also modified by taking the e-market
changes into account, and the desire plays as a criterion (i.e., independent on e-market situations) to help the agent to make decision
on actions from possible options. For example, once a buyer agent
decides its desire to complete the negotiation with car seller agents,
without changing the desire, the buyer agent can automatically
modify its negotiation behaviors when the market situation changes,
i.e., the buyer agent will give more concession to the seller agents
and accept a seller's price when the market is the seller's market.
However, when the market becomes the buyer's market, the buyer
agent will give less concession and may reject the same offer. That
is because when the market situation changes, the previous attractive offers may become not attractive anymore, and the proposed
model can take this dynamic changing into account. In the following
subsections, the proposed model will be introduced in aspects of
offer evaluation, counter-offer generation, and negotiation behavior
decision.
2. Desire-based negotiation model
2.2. Offer evaluation
In this section, we introduce a negotiation model for agents
bargaining in open and dynamic e-markets. The proposed model can
capture the dynamic changes of e-markets, and allows agents to modify
their negotiation behaviors based on their desires in completing a negotiation. Because agents' desires play as an important factor in deciding
agents' negotiation behaviors, we name the model as the desire-based
negotiation model.
In this subsection, we introduce an offer evaluation approach by
considering both e-markets' and agents' situations. The consideration
on e-markets' situations includes the number of buyers, the number
of sellers and the agent's role; while the consideration on agents'
situations includes agents' initial offers, and the subjective attitude on
the e-market change.
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
2.2.1. Consideration of market situation
Before we introduce the offer evaluation approach, we define some
notations. Let tuple bs,c,oini,d,τ,α,β,λ> be an indicator employed by
agents during negotiation, where s (s > 0) denotes the number of
sellers, c (c > 0) denotes the number of buyers, oini denotes the agent's
initial offer, and d (0 ≤ d ≤ 1) denotes the agent's desire. When d = 0,
it indicates that the agent is not interested in completing a negotiation,
and when d = 1, it indicates that the agent must complete a negotiation and reach an agreement. τ is the negotiation deadline. α denotes
the agent's role in the negotiation, where α = −1 for buyers and
α = 1 for sellers. β denotes the agent's attitude on the e-market
changes and λ indicates the agent's bargaining strategy. In this paper,
we only consider the single issue negotiation in an e-market and assume that the quantity of the negotiated item between a buyer agent
and a seller agent is one. However, the number of buyers and sellers
could be more than one and dynamically changes.
Firstly, by considering the number of buyer and seller agents in an
e-market, the relationship between supply and demand of the
e-market at a certain moment is represented as follows:
Φðs; c; α Þ ¼
c−s
α:
cþs
ð1Þ
The range of Formula (1) is in-between [− 1, 1], and represents
the status of an e-market. Intuitively, if 0 b Φ ≤ 1, the e-market is a
beneficial market (i.e., agents whose role is α will have advantages
in such a market); if − 1 ≤ Φ b 0, the e-market is an inferior market
(i.e., agents whose role is α will have disadvantages); if Φ = 0, the
e-market is an equitable market (i.e., all agents do not have any advantages or disadvantages). Objectively, Formula (1) represents the
relationship between supply and demand in an e-market at a certain
moment. For agents in different roles, their market situations are
also different. For example, when buyers are more than sellers
(c > s), for sellers (α = 1), because Φ(s,c,α) > 0, the market is beneficial to sellers. But for buyers (α = − 1), because Φ(s,c,α) b 0, the
market is inferior.
Objectively, Eq. (1) represents the relationship between supply
and demand in the negotiation environment at a certain moment.
However, even for the same e-market situation, agents may also
have their own considerations based on individual judgments. Therefore, we generate a graph (see Fig. 1) to indicate the relationship between an e-market's situation and an agent's response. In Fig. 1, the
x-axis represents situations of the e-market (Φ), and the y-axis indicates the agent's response. In general, when the e-market situation
shifts away from the equitable state to the beneficial or the inferior
state, the agent's response will move from calmness to vehemence.
In detail, it can be seen that agents may have three typical attitudes
in response to changes of the e-market.
• Cautious (β > 1): when the e-market situation shifts away from equitable to beneficial or inferior, the agent's response is calm when
changes of the e-market are not significant. However, when the
changes of the e-market become evident, the agent's response becomes more vehement.
• Acuminous (1 > β > 0): when the e-market situation shifts away
from equitable to beneficial or inferior, the agent performs sensitively even though the change in the environment is not obvious.
However, the agent must control the strength of its response due
to objective reasons such as the agent cannot make further concession anymore.
• Normal (β = 1): when the e-market situation shifts away from equitable to beneficial or inferior, the agent's response is also moved
from calmness to vehemence reposefully.
Even though the above three typical responses cannot cover all possible situations of an agent's response on e-market changes, the types of
responses can still be expressed. Based on the above description, we
57
Fig. 1. Negotiants' responses to markets' situations.
generate the following mapping function from an e-market's state to
an agent's response:
(
Ψðs; c; α; βÞ ¼
Φðs; c; α Þβ ;
−½−Φðs; c; α Þβ ;
Φðs; c; α Þ≥0
Φðs; c; α Þb0
ð2Þ
where Ψ∈[−1,1], s, c and α are defined in Eq. (1). The result of Ψ
indicates an agent's individual judgment about the e-market's
situation. Different agents may have different judgments on the same
e-market. When Ψ > 0, an agent estimates the e-market in a beneficial
state, when Ψ = 0, an agent estimates the e-market in an equitable
state, and when Ψ b 0, an agent estimates the e-market in an inferior
state.
However, because Ψ only takes into account an e-market situation,
we also propose the following function to consider the agent's individual situation in the offer evaluation.
2.2.2. Consideration of negotiant's situation
Let ol denote an offer from an opponent and oini denote an agent's
initial offer, then ol is firstly evaluated as a utility by the agent as follows:
o −oini
Λðol ; oini ; γ Þ ¼ th l
γ þ1
oini
ð3Þ
where γ = −1 indicates that the agent prefers a lower value than the
initial offer, γ = 1 indicates that the agent prefers a greater value
than the initial offer, and th(x) is defined as follow.
x
thðxÞ ¼
−x
e −e
ex þ e−x
ð4Þ
x
−x
x
−x
where thðxÞ ¼ ee −e
is the Hyperbolic Tangent Function (th(0) = 0,
þe
th(x) limits to 1 when x approaches infinite, and th(x) limits to −1
when x approaches negative infinite). The reason for selecting the Hyperbolic Tangent Function to map an offer to a utility value is that it
can effectively map any value to a value in-between the range [−1,
1], and the mapping function also accords with human's nonlinear attitude on value changes.
The result of Eq. (3) (Λ∈(0,2)) indicates how a negotiant's initial
offer is satisfied by the opponent's offer ol. For example, if the negotiant
plays as a buyer (i.e., α = −1), when ol = oini, then Λ = 1. It means
that the buyer's original expectation is fully satisfied. When ol > oini,
then 0 ≤ Λ b 1, it indicates that the buyer's original expectation can
only be partially achieved. And when ol b oini, then 1 b Λ b 2, it implies
that the buyer's expectation is overachieved. It must be pointed out that
the traditional offer evaluation approach [12] actually normalizes a
58
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
given offer within interval [0, 1] by using the initial offer and the reservation offer. However, our evaluation approach does not use the reservation offer, because agents may dynamically change their reservations
when the e-market situation changes. Such a feature also accords with a
human's habit in many real-world situations.
2.2.3. Considerations of both market and negotiant's situation
Because Eq. (3) only evaluates an offer based on an agent's initial
offer but does not take the e-market situation into account, the evaluation result may not accord with the market. Therefore, we modify the
offer evaluation function by considering both market and negotiant situations as follows:
Θðol ; s; c; oini ; α; β; γÞ ¼ Λðol ; oini ; γ Þ ð1−Ψðs; c; α; βÞÞ
ð5Þ
where the result of Eq. (5) indicates the negotiant's utility by accepting
the offer ol in a certain market. If it is an equitable market (Ψ = 0 and
Θ = Λ), then the offer ol is evaluated unbiasedly. If it is in a beneficial
market (0 b Ψ b 1 and Θ b Λ), then the offer ol is undervalued. And if
it is in an inferior market (−1 b Ψ b 0 and Θ > Λ), then the offer ol is
overvalued.
For example, a potential car purchaser's initial offer is $6000 and the
seller's offer price is $6500. Without consideration of the market situation, the buyer's evaluation result on the offer $6500 is Λ = 0.92, i.e.,
the buyer is 92% satisfied with the seller's offer. However, when taking
the market situation into account, results might be different. If the market is a buyer's market (for example, 5 buyers and 10 sellers, then Ψ =
0.33), the buyer's satisfaction on the offer $6500 will decrease to 61%
and the buyer may reject the offer. That is because in the buyer's market, a buyer has opportunities to make greater profits. On the other
hand, if the market is a sellers' market (for example, 10 buyers and 5
sellers, then Ψ = −0.33), the buyer's satisfaction on the offer $6500
will increase to 122%. It indicates that the buyer is very happy about
the offer $6500 in a disadvantageous market and may accept the offer.
During negotiation, desire-based agents will make decisions on their actions based on the result in Eq. (5) and their desire (see Section 2.4 for
details). In the following, we simplify the expression in Eq. (5) to Θ(ol).
2.3. Counter-offer generation
In the previous subsection, we introduce the approach to evaluate
opponent's offers by considering both the market's and the agent's
situations. In this subsection, we introduce a counter-offer generation
approach. The counter-offer generation approach also takes both the
market's and the agent's situations into account. Before we introduce
this approach, we define some notations.
→
Let set O t denote all offers that an agent received from its opponents
→
in round t, obt denotes the ‘best’ offer in O t (i.e., the offer brings the
highest profit to the agent, obt ¼ arg max → fΘðot ; s; c; oini ; α; β; γÞg),
→
Ot
ow
t
ot ∈O t
denotes the ‘worst’ offer in
(i.e., the offer brings the lowest profit
to the agent, obt ¼ arg min → fΘðot ; s; c; oini ; α; β; γÞg), om
t denotes the
→
of O t
ot ∈O t
∑Ni¼1 oit
→
set O t ), obt′
Fig. 2. Counter-offer generation.
1
(i.e., om
and N is the size of
denotes
average
t ¼N
the estimated best offer in the next round t′, cot denotes the agent's latest counter-offer, and cot ′ denotes the agent's counter-offer for the next
round. Then if an agent plays as a buyer, one possible situation of the
counter-offer generation procedure in the negotiation round t is illustrated in Fig. 2.
In Fig. 2, the x-axis stands for prices and the y-axis stands for the
occurrence density
on each price. The solid curve indicates the distri→
to case,
bution of set O t in the round t, which may differ from case
→′
and the dotted line is the estimated distribution of set O t in the
next round. We make
the assumption
that the shape of the distribu→′
→0
tion curve of set O t is similar to O t s, but just the domain is changed.
Because the agent plays as a buyer, so the market represented
in
→′
Fig. 2 is a beneficial market. In→a beneficial market, for buyers, O t is
estimated to be smaller than O t on average. The distance between
the current counter-offer cot and the estimated ‘best’ offer obt′ in the
next round is the bargaining area. The new counter-offer cot ′ is generated within this area according to the agent's negotiation strategy,
the e-market's situation, and the time constraint.
Firstly, we estimate the ‘best’
offer obt′ in the next round t′ by consid→
ering both the distribution of O t and the e-market's situation as follows:
b
ot ′
¼
b
ot
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
→
þ Ψðs; c; α; βÞ 3 D O t γ
ð6Þ
X
2
N →
→
ot;i −E O t
pi
D Ot ¼
ð7Þ
i¼1
→
→
where D O t indicates the variance of O t , γ = −1 for issues which an
agent prefers a lower value and γ = 1 for issues which an agent prefers
→
→
a greater value, E O t indicates the mathematical expectation of O t , pi
indicates the distribution of ot,i and Ψ(s,c,α,β) indicates the agent's
response to the e-market's situation. We set the maximal possible
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
→
change of the expected best offer to 3 D O t because 99% of
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
#
→
→
−3 D O t ; 3 D O t
in
"
observed value locates in interval
→
mathematics. Usually, when the distribution of O t is a Gaussian
→
1
distribution, then E O t ¼ om
t , pi ¼ N and Eq. (7) is specified as:
∑N o −om 2
→
i¼1
t
t;i
:
D Ot ¼
N
ð8Þ
Then the counter-offer cot ′ for the following negotiation round is
generated as follows:
cot ′ ¼
8
< oini ;
when t ¼ 0;
1λ
b
; when 0bt≤τ:
: cot þ ot ′ −cot τ
ð9Þ
where oini is the agent's initial offer, cot is the agent's current
counter-offer, obt′ is the estimated ‘best’ offer in the next round, and
we simply adopt parameter λ in Faratin et al.'s model [7] to represent
the agent's bargaining strategies.
In Fig. 3, it can be seen that when the e-market becomes more beneficial to the buyer agent, it is possible that obt′ bcot and cot′ bcot . So in
the desire-based negotiation model, we propose a decommitment
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
59
desire-based negotiation model based on Rubinstein's alternating
offers protocol [7] as follows.
Fig. 3. Counter-offer generation.
mechanism which allows agents to reject previous offers if the offers
are not formally accepted by any opponents. The reason that we propose such a mechanism is because in the desire-based negotiation
model, both the offer evaluation approach and counter-offer generation
approach are impacted by the e-market's situation. So when the
e-market's situation changes, agents may change their considerations
on both the offer evaluation procedure and the counter-offer generation
procedure in order to gain more profits. For example, buyers may generate disadvantageous counter-offers when the e-market is inferior.
However, when buyers notice that the e-market may become beneficial
and if previous counter-offers are not accepted by any seller, buyers can
reject the previous disadvantageous counter-offers and re-generate advantageous counter-offers in order to enlarge their profits. On the other
hand, if sellers notice that the e-market may become inferior for them in
advance, they may accept buyers' current offers in order to avoid losses
in the future.
Also, the e-market may become inferior for buyers. In Fig. 4, it can
be seen that when a market is inferior for buyers, the estimated ‘best’
offer for the following round is worse than the ‘best’ offer in the
round t, i.e. obt′ > obt . During negotiations, if the new counter-offer
in the round t′ can bring more profits to the
agent than the ‘best’
offer in the current round t, i.e. Θðcot ′ Þ > Θ obt , the agent will keep
on bargaining with opponents and send out the new counter-offer
cot ′ . However, if the new counter-offer is worse than the ‘best’
offer, i.e. Θðcot ′ ÞbΘ obt , (see the case shown in Fig. 4), the agent
will not send the new counter-offer cot ′ , but make its final decision
about the negotiation based on the comparison between the ‘best’
offer (obt ) from opponents and the agent's desire (d). The detailed encounter rule of the desire-based negotiation model is introduced in
the following subsection.
2.4. Negotiation protocol
Since both the offer generation approach and the counter-offer
evaluation approach have some differences from the classic negotiation models [7,15,28], we propose a negotiation protocol for our
Fig. 4. Counter-offer generation.
• Step 1 The agent assigns negotiation parameters, i.e., initial offer (oini),
desire (d), negotiation deadline (τ), role in negotiation (α), attitude on
e-market's situation changes (β) and bargaining strategy (λ). The
number of consumers (c) and suppliers (s) can be obtained from the
e-market directly. Also the agent initializes t to 0 and cot to oini.
• Step 2 The agent broadcasts cot to all opponents and waits for responses.
• Step 3 Once the agent gets responses, if any opponent accepts cot, the
negotiation is completed. Otherwise, if t > τ, the procedure goes on
to Step 4; and if t ≤ τ, the procedure goes on to Step 5.
• Step 4 Because the agent does not have time for further bargaining, it
has to make a final decision on the ‘best’ offer obt in the last round. The
criterion of the decision making is the agent's desire. A higher desire
indicates more eagerness to complete a negotiation, and the agent
would like to make more concession in order to reach an agreement.
To the contrary, a lower desire indicates less eagerness to complete a
negotiation, and the agent would like to get more benefit from an
agreement. Therefore, the comparison between the evaluation on
the ‘best’ offer obt (Θ(obt )) and the agent's threshold on its profit for a
particular desire (1 − d) should be considered. If Θ(obt )1 ≥1 − d,
the agent will accept obt and the negotiation is completed. Otherwise,
the negotiation fails.
• Step 5 Because the agent still has time for further bargaining, so the
agent will generate a new counter-offer cot ′ for the next round. In this
situation, the agent should compare its profit from the ‘best’ offer obt
(i.e., Θ(obt )), the profit from its counter-offer cot ′ (i.e., Θðcot ′ Þ), and its
minimal acceptable profit
d (i.e., 1 − d) before
for
desire
making the decision. For details, if max Θ obt ; Θðcot ′ Þ; 1−d ¼ Θ obt , the offer obt will
be accepted by the agent and the negotiation is completed. If
max(Θ(obt ), Θðcot ′ Þ; 1−dÞ ¼ 1−d, the agent will leave off the procedure and the negotiation fails. If max(Θ(obt ), Θðcot ′ Þ; 1−dÞ ¼ Θðcot ′ Þ,
the procedure goes on to Step 6.
• Step 6 The agent updates t to t′, cot to cot ′ and parameters c, and s
according to the current market situation, then the procedure goes
back to Step 2.
Based on the above procedure, the agent's action in round t is defined as follows:
8
>
>
Quit; t ≥ τ ∧ Θ obt b1−d or
>
>
>
>
b
>
>
> t b τ ∧ max Θ ot ; Θðcot ′ Þ; 1−d ¼ 1−d;
>
<
Ωðt Þ ¼ Accept obt ; t ≥ τ ∧ Θ obt ≥ 1−d or
ð10Þ
>
>
>
b
b
>
>
t b τ ∧ max Θ ot ; Θðcot′ Þ; 1−d ¼ Θ ot ;
>
>
>
>
>
: Offer cot ′ ; t b τ ∧ max Θ obt ; Θðcot ′ Þ; 1−d ¼ Θðcot ′ Þ:
In Eq. (10), it can be seen that the final agreement reached by the
proposed model is Pareto efficient. That is because if an agent accepts
its opponent's offer as an agreement, then according to the acceptance
condition, the opponent's offer must be better than the agent's all
counter-offers in the remaining negotiation rounds. Therefore, the
agent's profit by accepting the opponent's offer is the maximal profit
that the agent may get from the negotiation, and it is impossible to further enlarge the agent's profit without damaging the opponent's profit.
Because there are no other offers that will make the agent better off
without making the opponent worse off, the final agreement generated
by the proposed model is Pareto optimal.
In this section, we introduced a desire-based model for e-market negotiation by considering the dynamic changes of supply and demand in
an e-market. Firstly, a fair evaluation of an e-market was proposed to
1
Simplification of Eq. (5).
60
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
indicate the objective supply and demand situation in the e-market.
Both buyers and sellers were equally considered in the evaluation,
and played the same importance. Secondly, each agent's subjective response was calculated by considering the agent's attitude on the
e-market situation changes, and was taken into account in both offer
evaluation and counter-offer generation procedures. Lastly, a fair negotiation protocol was proposed to ensure the equilibrium of the negotiation between buyers and sellers. Therefore, the proposed desire-based
model is a non-bias negotiation model, and played fairly in-between
buyers and sellers.
rounds (ANR), average negotiation time (ANT, in millisecond), and average agreement number (AAN). The BAU, SAU, and AAU are calculated as
follows.
3. Experiments
BAU ¼
Sum of all successful buyers0 utilities
Number of agreements
ð11Þ
SAU ¼
Sum of all successful sellers0 utilities
Number of agreements
ð12Þ
AAU ¼
Sum of all successful agents utilities
:
Number of agreements
0
In this section, we illustrate the experimental results of our desirebased negotiation model, and compare the results with the classic
NDF negotiation model [7]. Section 3.1 introduces the experimental
setup. Section 3.2 demonstrates the experimental results. In Section
3.3, we analyze the experimental results and present further discussion
on the proposed model.
3.1. Experiment setting
In order to mimic situations of an e-market, we set the maximal
agent number to 50, including 25 buyer agents and 25 seller agents. In
order to mimic a dynamic e-market, the negotiation agents' number
for both buyers and sellers are randomly selected in between 1 and 25,
and are dynamically changed during the negotiation. Therefore, the
rates of buyers and sellers vary in between 1 : 25 and 25 : 1. The negotiation issue is cars' prices. For the buyer agents, their initial prices are
randomly selected between $1500 and $4500, reservation prices are
randomly selected between $5000 and $15,000. For the seller agents,
their initial prices are randomly selected between $5000 and $15,000,
reservation prices are randomly selected between $1500 and $4500.
For all negotiation agents, parameters for their negotiation strategy are
randomly selected in interval [0, 2], their negotiation deadlines are randomly selected in interval [15, 25]. The final negotiation parameters for
25 buyers are displayed in Fig. 5, and the final negotiation parameters for
25 sellers are displayed in Fig. 6. In order to clearly show the performance of negotiation models, we analyze six experimental results, in
terms of the buyers' average utility (BAU), the sellers' average utility
(SAU), all negotiation agents' average utility (AAU), average negotiation
ð13Þ
3.2. Experimental results
In order to display the performance of our negotiation model, we
will carry out three experiments. In the first experiment, both the
buyer and seller agents employ the classic NDF negotiation model [7]
(that cannot handle the dynamics of e-market situations); and in the
second experiment, the buyer agents will employ our negotiation
model, but the seller agents still employ the classic negotiation model;
and in the third experiment, both the buyer and seller agents will employ our negotiation model. In all experiments, both the buyer agents'
and the seller agents' numbers are started from 1, and gradually increased to 25.
3.2.1. All agents employ the classic model
In Fig. 7, we illustrate the first experimental results. The x-axis indicates the buyer agent's number, and the y-axis indicates the seller
agent's number. It can be seen that by comparing with the SAU (see
Fig. 7(b)), the BAUs (see Fig. 7(a)) are relatively low. Such differences
are caused by different negotiation parameters between buyer and
seller agents, i.e., initial prices, reservation prices, negotiation strategies, and deadlines. The AAUs (see Fig. 7(c)) are the sum of the buyer
and seller agents' utilities. Generally, when the e-markets become
more complex, i.e., the agents' number increases, agents will spend
more ANR (see Fig. 7(d)) and ANT (see Fig. 7(e)) in order to achieve
agreements. Also, the AAN will be increased when the agents' number
becomes large (see Fig. 7(f)).
Fig. 5. Buyer agents' negotiation parameters.
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
61
Fig. 6. Seller agents' negotiation parameters.
Furthermore, in order to help readers to understand agent's negotiation behaviors, in Fig. 8 we display the detailed negotiation process in different e-market's situations (i.e., the beneficial market, the
equitable market, and the inferior market) when the maximum
agent number is six (i.e., three buyer agents and three seller
agents). The x-axis indicates the negotiation round, and the y-axis
indicates agents' offer on the car's price. The legend nb indicates
the buyer agents employing the classic negotiation model, and the
legend ns indicates the seller agents employing the classic negotiation
model. Both the buyer agent and the seller agent's numbers are gradually increased from 1 to 3. It can be seen in Fig. 8 that when the negotiation environment changes, both the buyer agents and the seller agents
a
1
0.6
0.4
0.2
Total utility
0.8
Seller utility
0.8
c
Classic model
Classic model
Buyer utility
3.2.2. Only buyer agents employ our model
In the second experiment, all buyer agents employ our negotiation
model, and all seller agents employ the classic negotiation model. In
order to ensure all buyer agents would like to complete negotiations,
b
1
0.6
0.4
0.2
0
25
0
25
Se 20
ller 15
nu
mb 10
er
5
5
10
15
Se 20
ller 15
nu
mb 10
er
25
20
ber
m
er nu
Buy
d
5
5
10
r
mbe
u
yer n
Bu
20
ller
15
nu
mb
10
er
5
5
10
15
25
20
r
Buye
be
r num
Agreement number
25
Se
25
100
Classic model
80
60
40
20
0
25
20
Se
ller
15
nu
10
mb
er
5
5
15
25
20
er
mb
er nu
10
Buy
f
Classic model
20
18
16
14
12
10
8
6
4
2
Classic model
Se 20
ller 15
nu
mb 10
er
25
20
15
1.6
1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
25
e
Negotiation time
Negotiation round
fail to capture the e-market changes, and cannot adapt their negotiation
behavior dynamically. For example, the final agreements achieved between the buyer agent nb1 and the seller agent ns1 are exactly the
same (i.e., 8476) in different e-market's situations (see Fig. 8(a) and
(b)). Also, the final agreements achieved between the buyer agent nb2
and the seller agent ns1 are exactly the same (i.e., 10,843) in different
e-market's situations (see Fig. 8(d), (e), (g) and (h)).
5
5
20
10
15
25
r
mbe
Buy
er nu
Fig. 7. Negotiation results of the classic negotiation model.
Classic model
20
15
10
5
0
25
Se 20
ller 15
nu
mb 10
er
5
5
15
20
ber
um
yer n
10
Bu
25
62
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
Fig. 8. Negotiation results of the classic negotiation model.
we set the buyer agents' desire to the highest level (i.e., ε = 1). In order
to simplify the experiment, we set the buyer agents' attitudes on market
changes to normal (i.e., β = 1). Because our negotiation model uses different offer evaluation approaches from the classic negotiation model,
in order to easily compare the experimental results, we employ the classic offer evaluation approach to re-evaluate the final agreements
achieved by using our negotiation model. So the experimental results illustrated in Figs. 7, 9, and 11 can be compared directly.
The second experimental results are illustrated in Fig. 9. It can be
seen that BAUs (see Fig. 9(a)) show different values in different market
situations. When it is an equitable market (i.e., buyer number = seller
number), BAUs are similar as the values gained in the first experiment.
However, when the market becomes more beneficial to the buyers
(i.e., buyer number b seller number), BAUs increase gradually. The
maximum BAU is around 1, and appears when there are 25 sellers but
only 1 buyer in the market. On the other hand, when the market becomes inferior to the buyers (i.e., buyer number > seller number),
BAUs decrease gradually. In the extreme case, when the market contains
only 1 seller but 25 buyers, BAU is minimized and almost equals to −0.5
(i.e., the final agreement is worse than the reservation offer in the classic model). The reason for such differences is because the buyer agents
adapt their negotiation behaviors when the e-market's situation
changes, and try to enlarge profits in beneficial markets, but to give
more concessions in inferior e-markets.
Even though the seller agents cannot adapt their negotiation behaviors initiatively, SAUs (see Fig. 9(b)) are also varied in different market
situations with the changes of the buyer agents' behaviors. In general,
SAU is increased from 0 to 1 when the e-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
reach agreements, the buyer agents have to make great concessions in
a seller's market, so the seller agents' profits are increased.
AAUs (see Fig. 9(c)) are increased around 0.2 on average by comparison with the outcomes of classic negotiation model (see Fig. 7(c)). Such
an increment implies that our negotiation model can improve the outcome of the whole market in different e-market situations.
In a buyer's market, the buyer agents would like to spend more
time on bargaining in order to maximize their profits, and so ANRs
(see Fig. 9(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 negotiation model could spend more time than the classic negotiation model (see Fig. 9(e)).
According to the experimental setup, since the bargain areas exist
between all buyer and seller agents, the classic negotiation model can
reach agreements between all buyer agents and seller agents theoretically. 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 slight decrement
on AAN by using our negotiation model (see Fig. 9(f)).
In Fig. 10, we also display the detailed negotiation process for six
agents. Legend db indicates the buyer agent employing our desirebased negotiation model. It can be seen that when the negotiation contains only two agents (see Fig. 10(a)), the agreement reached between
the buyer agent db1 and the seller agent ns1 is 7745. When the
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
a
63
b
c
1.5
2
1
1.5
0
−0.5
−1
25
1
0.5
0
5
5
20
10
15
Se 20
ller 15
nu
mb 10
er
25
er
umb
rn
Buye
1
0.8
0.6
5
5
10
15
20
20
Se
ller 15
nu 10
mb
er
ber
r num
Buye
e
Our model
120
Negotiation time
20
18
16
14
12
10
8
6
4
2
25
Se 20
ller 15
nu
mb 10
er
1.2
25
Our model
25
100
80
60
40
20
0
25
5
5
10
15
25
20
r
Buye
be
r num
5
5
15
25
20
r
be
r num
10
Buye
f
Agreement number
d
1.4
0.4
25
−0.5
25
Se 20 15
ller
nu
mb 10
er
Negotiation round
1.6
Total utility
0.5
Our model
1.8
Our model
Seller utility
Buyer utility
Our model
Se 20
ller 15
nu
mb 10
er
5
5
10
15
Our model
20
15
10
5
0
25
25
20
r
be
r num
Buye
20
Se
ller 15
10
nu
mb
er
5
5
15
20
25
ber
um
yer n
10
Bu
Fig. 9. Negotiation results of our negotiation model.
negotiation contains one more seller agent (see Fig. 10(b)), the buyer
agent db1 notices such a change in the e-market, and makes less concession in each negotiation round. The final agreement reached between
the buyer agent db1 and the seller agent ns1 is 7589. Obviously, the
buyer agent's profit is increased in a beneficial market. Furthermore,
when the market becomes more beneficial (see Fig. 10(c)), the buyer
Fig. 10. Negotiation results of the classic negotiation model.
64
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
agent db1's final agreement is only 3798. Such a result justifies that our
negotiation model can help agents to increase profits in the beneficial
markets by comparison with the classic negotiation model.
However, when the market becomes inferior, the buyer agents need
to pay more in order to compete with other buyers. For example, in Fig.
10(h) the market contains three buyer agents and two seller agents, by
using the classic negotiation model, the agreement reached between
the buyer agent nb2 and the seller agent ns1 is 10,843; the agreement
reached between the buyer agent nb3 and the seller agent ns2 is
7796; and the buyer agent nb1 fails the negotiation. By using our negotiation model (see Fig. 10(h)), the agreement reached between the
buyer agent db2 and the seller agent ns1 becomes 12,298 (i.e., the
buyer agent db2 loses profit by comparing to the buyer agent nb2);
the agreement reached between the buyer agent db1 and the seller
agent ns2 becomes 8832; and the buyer agent db3 fails the negotiation.
It can be seen that by employing our negotiation model, the buyer agent
db1 beats the buyer agent db3 through making more concession to the
seller agent ns2 (original, the buyer agent nb3 beats the buyer agent nb1
in the classic negotiation model).
3.2.3. All agents employ our model
In the third experiment, all agents employ our negotiation model,
and the experimental results are illustrated in Fig. 11. Legend ds indicates the seller agents employing our desire-based model. It can be
seen that after both buyer and seller agents employ our negotiation
model, the BAU (see Fig. 11(a)) is increased more in the buyer's market
and decreased more in the seller's market. That is because both the
buyer and seller agents are aware of the e-market's situation change,
and try to maximize their profits in the beneficial e-markets, and to
give more concessions in the inferior e-markets. By contrary, for the
same reason, the SAU (see Fig. 11(b)) is increased more in the seller's
market and decreased more in the buyer's market. The AAU
(see Fig. 11(c)) becomes more balanced between the buyer's and the
seller's market by comparing with the result in the second experiment
(see Fig. 9(c)). The ANR (see Fig. 11(d)) shows a big difference by comparing with the previous result (see Fig. 9(d)). The ANR increases in
a
both the buyer's and the seller's market, and the maximal ANR appears
in the equitable market. That is because in order to increase profits, the
buyer agent would like to negotiate more in the buyer's market, the seller
agent would like to negotiate more in the seller's market, and both the
buyer and seller agents need to bargain more in the equitable market. Because agents need more negotiation rounds before agreements can be
achieved, they will spend more time in negotiations as well. It can be
seen that the ANT (see Fig. 9(e)) is increased on average, and is maximized in the most complex market situation (i.e., the market contains
50 agents). Finally, Fig. 11(f) shows the ANN. It can be seen that by
using our negotiation model, the ANN is improved by comparison with
the previous two experiments (see Fig.s. 7(f) and 9(f)), and reaches the
maximal value in all market situations.
In Fig. 12, the detailed negotiation procedures for maximal six
agents are illustrated. Both the buyer and the seller agents employ
our negotiation model. By comparison with the previous experiment
results (see Fig. 10), the buyer agents' profits are improved in the
buyer's market, and the seller agents' profits are improved in the
seller's market. Such a result accords with the result displayed in
Fig. 11(a) and (b). For example, when the market contains only 1
buyer agent and 3 seller agents (i.e., a buyer's market), if all agents
employ the classic negotiation model, the agreement achieved between the buyer agent nb1 and the seller agent ns3 is only 6474
(see Fig. 8(c)); if only the buyer agent employs our negotiation
model, the agreement achieved between the buyer agent db1 and
the seller agent ns2 is improved to 3798 (see Fig. 10(c)); and if all
agents employ our negotiation model, the agreement achieved between the buyer agent db1 and the seller agent ds2 is further improved to 3057 (see Fig. 12(c)). Therefore, the buyer agent db1's
profit is increased in the buyer's market by using our negotiation
model. On the other hand, when the market contains 3 buyer agents
and only 1 seller agent (i.e., a seller's market), if all agents employ the
classic negotiation model, the agreement achieved between the buyer
agent nb2 and the seller agent ns1 is only 10,843 (see Fig. 8(g)); if
only the buyer agent employs our negotiation model, the agreement
achieved between the buyer agent db2 and the seller agent ns1 is improved to 12,339 (see Fig. 10(g)); if all agents employ our negotiation
b
c
Our model
Our model
Seller utility
Buyer utility
1
0.5
0
−0.5
−1
−1.5
−2
25
Se 20 15
ller
nu
mb 10
er
5
5
10
15
25
20
1.5
1.2
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
25
Our model
ller
Buye
Our model
Se 20
ller 15
nu
mb 10
er
0
−0.5
15
nu
mb 10
er
5
5
10
15
20
25
20
Se
ller 15
nu 10
mb
er
r
be
r num
Buye
e
Agreement number
25
80
60
40
20
0
25
5
5
10
15
20
er
Buy
mb
er nu
25
20
Se
5
5
10
15
25
20
r
be
r num
Buye
f
Our model
100
Negotiation time
Negotiation round
d
20
18
16
14
12
10
8
6
4
2
25
0.5
−1
25
20
Se
r
be
r num
1
Total utility
1.5
ller 15
nu 10
mb
er
5
5
10
15
25
20
r
be
r num
Buye
Fig. 11. Negotiation results of our negotiation model.
Our model
20
15
10
5
0
25
Se 20 15
ller
nu
mb 10
er
5
5
10
15
25
20
r
Buye
be
r num
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
65
Fig. 12. Negotiation results of the classic negotiation model.
model, the agreement achieved between the buyer agent db2 and the
seller agent ds1 is further improved to 13,631 (see Fig. 12(g)). Therefore, the seller agent ds1's profit is increased in the seller's market by
using our negotiation model.
3.3. Discussions
In the previous subsection, we illustrated experimental results in
different market situations. It can be seen that when the e-market's
situations change, our negotiation model can help agents to modify
their negotiation behaviors dynamically. Also, even for the same
e-market's situation, agents' behaviors may also be different when
they have different desires on trading. Therefore, both e-market's
situations and agents' desires will impact negotiation results. In
this subsection, we discuss how these two factors affect agents'
behaviors in negotiations.
In Fig. 13, we illustrate a model to demonstrate how the e-market's
situation and the agent's desire impact agents' behaviors in
negotiations. The x-axis denotes the e-market's situation (refer to
Eq. (1)), the y-axis denotes the agent's desire, and the z-axis denotes the agent's evaluation on an offer (refer to Eq. (3)). Then by
setting both negotiation parameters β and λ to 1 (i.e., normal attitude on market change and linear negotiation strategy), a trading
surface for the desire-based negotiation model can be formulated
as follows:
ΓðΦ; dÞ ¼
ð1 þ ΦÞ ð1−dÞ; when−1≤Φ≤0;
ðΦ−1Þ d þ 1; when 0bΦ≤1
but reject offers below the surface. For the trading surface of our
desire-based negotiation model, in an extreme case, when Φ = −1
or d = 1 the threshold is Γ(Φ,d) = 0, so the agent will accept the
‘best’ offer from its opponents finally in order to make the deal. That is
because when Φ = −1, the market is extremely disadvantageous for
the agent, so any offer will be considered as a ‘good’ offer based on
the market situation; and when d = 1, the agent needs to complete
the negotiation extremely, so the agent will accept the ‘best’ offer
from its opponents finally. In another extreme case, when Φ = 1 or
d = 0, the threshold is Γ(Φ,d) = 1, so the agent will reject any offer
which cannot satisfy its initial offer. That is because when Φ = 1, the
e-market is extremely advantageous for the agent, so any offer below
the agent's initial offer will be considered as a ‘bad’ offer; and when
ð14Þ
where d∈[0,1] and Φ∈[− 1,1].
The trading surface defines a set of thresholds on agent's profits.
During the negotiation, agents will accept offers above or on the surface,
Fig. 13. Trading surface of negotiation models.
66
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
d = 0, the agent's motivation for completing the negotiation is very
low, so any offer worse than the agent's initial offer definitely will be
rejected by the agent. In a normal case, such as Φ = 0 and d = 0.5
(i.e. an equitable market and the agent hesitates about trading), the
agent will not accept any offer which cannot meet its satisfaction by
50%.
Also, we display another trading surface for the classic negotiation
model. In comparison with the desire-based model, the classic model's
trading surface is just a plane surface. That means the agent in the classic model will fix its thresholds in all situations into a constant, and does
not consider changes of markets and agent's desires for trading. It can
be seen in Fig. 13 that an instance of the trading surface for the classic
model (Λ = 50%) is partially below the trading surface of our model
and partially above our model. For agents using the classic model,
they will accept all offers on this surface. However, for agents using
our model, situations are more complex. When Φ > 0 (i.e., a beneficial
market) and d b 0.5 (i.e., agents do not really want to make a deal),
agents will not accept offers which are located on the classic model's
trading surface. On the other hand, when Φ b 0 (i.e., an inferior market)
and d > 0.5 (i.e., agents want to make a deal), agents will accept offers
which locate on the classic model's trading surface.
4. Related work
Some related works also take into account agent negotiation in
complex environments. This section discusses differences between
these related works and our model.
An et al. [1] proposed a concurrent negotiation model to coordinate
interrelated negotiations in Electronic Commerce markets where
agents need to negotiate with different opponents for multiple resources. During a concurrent negotiation, an agent negotiates with different opponents on different resources, and adjusts its negotiations
according to the market conditions and negotiation situations. If it is
necessary, the agent can also decommit its tentative agreements by
paying a penalty. Because the agent may have different deadlines and
expectations on different resource negotiations, both the time constraints and the expected agreement prices are considered for each negotiation. Also, the maximum number of final agreements is considered
to evaluate the overall negotiation. By comparison with their work, our
paper considers the supply and demand of an e-market and the multiple preferences on negotiation issues.
He et al. [14] proposed a very successful model for trading agents in
solving issues in supply chain management. Firstly, the customer agent
in their model collected customer requests and sorted them by agent's
profits gained from each customer. Then according to customers' requirements, such as type of item, reserved price, penalty and due
time, the customer agent makes a decision about the order of servers.
In order to increase the trading agent's profit, the component agent predicts customers' requests in both the near term and distant future.
According to the prediction results, the trading agent keeps its own inventory in an appropriate level in order to ensure that adequate components can be provided for daily regular offers, as well as minimize the
storage expenditure. Finally, by employing the prediction results and
fuzzy reasoning, the trading agent can successfully handle issues of
offer generation, component booking and assembly, and PC delivery.
One significant difference between He's model and our proposed
model is that in the former model, competitions from other trading
agents are not taken into account. By contrast, in our proposed model,
we consider both trading opportunity and competition in real time.
Therefore, He's model is very suitable to solve issues in supply chain
management, while our model can yield efficiencies in dynamic multilateral bargaining.
Gregg and Walczak [13] proposed a decision support system for
online-auction. Besides buyer agents and seller agents, authors also
created several assistant agents, such as information retrieval agents,
data-analysis agents and information agents, to help auction participants
to improve the quality of their decision making. The assistant agents
can efficiently collect data related to the online auction, make further
statistical calculations and recommendations for the auction, and
generate additional auction rules by using data mining strategies.
Both simulated and real purchases at online auction indicate the
benefit that auction participants achieve by employing this auction
advisor system.
Ren et al. [26,27] proposed a market-driven model to help agents
to make concessions in negotiation. Four concession factors, namely
trading opportunity, trading competition, trading time and strategy and
eagerness, are introduced to represent both market and agent situations. Each concession factor impacts an agent's concession from a
certain consideration. All concession factors are updated by the
agent according to the market's dynamic situation. But agents' judgments on offers and expectations on negotiation outcomes are still
fixed. In this paper, we model markets by considering both market
situations and agent desires. During negotiations, agents make concessions based on both objective and subjective considerations in
the negotiation.
By comparison with the above related works, our negotiation
model has the following merits. It models negotiations in e-markets
by considering (1) both objective situations of markets and subjective
desires of agents, (2) both concurrent and future possible situations of
e-markets, and (3) both agents' individual profit and trade-offs of
whole e-market.
5. Conclusion and future work
In this paper, we proposed a desire-based negotiation model to
help agents to perform adaptive negotiation behaviors in e-markets
by considering both the e-market's situation and the agent's desire.
In our model, the offer evaluation approach and counter-offer generation approach take both the objective situation of e-markets and the
subjective situation of agents into account. Offers from opponents
are evaluated relatively by considering the e-market's situation and
counter-offers are generated through estimating the possible changes
of the e-market. Also, a negotiation protocol was proposed to define
the negotiation procedure in e-markets. In the experiment, we illustrate the performance of the proposed negotiation model in different
e-market situations. The experimental results well demonstrated
that our negotiation model can effectively capture the e-market situation changes, and modify agents' negotiation behaviors accordingly.
Furthermore, based on experimental results, we proposed the concept
of ‘trading surface’ and discovered that the trading surface of our negotiation model is more applicable than the classic model's in e-markets.
Our future work will focus on two aspects. The first consideration is
to extend the existing model from single issue negotiation to multiple
issue negotiation by considering both numerical and categorical issues.
The second consideration is to employ the Fuzzy and/or Neural network
approaches [3] to help agents to perform more adaptive negotiation behaviors in e-markets.
References
[1] B. An, V. Lesser, K. Sim, Strategic agents for multi-resource negotiation, Autonomous Agents and Multi-Agent Systems 23 (1) (2011) 114–153.
[2] Y. Bakos, The emerging role of electronic marketplaces on the Internet, Communications of the ACM 41 (8) (1998) 35–42.
[3] R. Carbonneau, G. Kersten, R. Vahidov, Pairwise issue modeling for negotiation
counteroffer prediction using neural networks, Decision Support Systems (2011)
449–459.
[4] H. Chandrashekhar, B. Bhasker, Quickly locating efficient, equitable deals in automated negotiations under two-sided information uncertainty, Decision Support
Systems 52 (1) (2011) 157–168.
[5] C. Cheng, C. Chan, K. Lin, Intelligent agents for e-marketplace: negotiation with issue
trade-offs by fuzzy inference systems, Decision Support Systems 42 (2) (2006)
626–638.
[6] S. Das, The Effects of Market-Making on Price Dynamics, 7th Int. Conf. on Autonomous Agents and Multiagent Systems (AAMAS08), 2008, pp. 887–894.
F. Ren, M. Zhang / Decision Support Systems 60 (2014) 55–67
[7] P. Faratin, C. Sierra, N. Jennings, Negotiation decision functions for autonomous
agents, Journal of Robotics and Autonomous Systems 24 (3–4) (1998) 159–182.
[8] S. Fatima, M. Wooldridge, N. Jennings, Multi-Issue Negotiation Under Time Constraints,
1st Int. Conf. on, Autonomous Agents and Multi-Agent Systems (AAMAS02), 2002,
pp. 143–150.
[9] S. Fatima, M. Wooldridge, N. Jennings, An agenda-based framework for multi-issue
negotiation, Artificial Intelligence 152 (1) (2004) 1–45.
[10] S. Fatima, M. Wooldridge, N. Jennings, Optimal negotiation of multiple issues in
incomplete information settings, 3rd Int. Conf. on Autonomous Agents and
Multiagent Systems(AAMAS04), 2004, pp. 1080–1087.
[11] S. Fatima, M. Wooldridge, N. Jennings, Approximate and online multi-issue negotiation, 6th Int. Conf. on, Autonomous Agents and Multi-Agent Systems (AAMAS07),
2007, pp. 947–954.
[12] S. Fatima, M. Wooldridge, N. Jennings, An analysis of feasible solutions for
multi-issue negotiation involving nonlinear utility functions, Proc. of 8th Int. Conf.
on Autonomous Agents and Multiagent Systems (AAMAS09), 2009, pp. 1041–1048.
[13] D. Gregg, S. Walczak, Auction Advisor: an agent-based online-auction decision
support system, Decision Support Systems 41 (2) (2006) 449–471.
[14] M. He, A. Rogers, X. Luo, N. Jennings, Designing a successful trading agent for supply chain management, 5th International Joint Conference on Autonomous
Agents and Multiagent Systems (AAMAS 2006), ACM, Hakodate, Japan, 2006,
pp. 1159–1166.
[15] N. Jennings, P. Faratin, A. Lomuscio, S. Parsons, C. Sierra, M. Wooldridge, Automated negotiation: prospects, methods, and challenges, International Journal of
Group Decision Negotiation 10 (2) (2001) 199–215.
[16] K. Kurbel, I. Loutchko, A model for multi-lateral negotiations on an agent-based
job marketplace, Electronic Commerce Research and Applications 4 (3) (2005)
187–203.
[17] G. Lai, C. Li, K. Sycara, A general model for Pareto optimal multi-attribute negotiations, 2nd Int. Workshop on Rational, Robust, and Secure Negotiations in
Multi-Agent Systems (RRS06), 2006, pp. 55–76.
[18] G. Lai, K. Sycara, C. Li, A. Pareto, Optimal model for automated multi-attribute negotiations, 6th Int. Conf. on, Autonomous Agents and Multi-Agent Systems
(AAMAS07), 2007, pp. 1040–1042.
[19] X. Li, L. Soh, Adaptive, confidence-based strategic negotiations in complex
multiagent environments, 9th Int. Florida Artificial Intelligence Research Society
Conf., 2006, pp. 80–85.
[20] M. Ma, Agents in E-commerce, Communications of the ACM 42 (3) (1999) 78–80.
[21] J. MacKie-Mason, A. Osepayshvili, D. Reeves, M. Wellman, Price prediction strategies for market-based scheduling, 4th Int. Conf. on Automated Planning and
Scheduling (ICAPS04), 2004, pp. 244–252.
[22] P. Maes, R. Guttman, A. Moukas, Agents that buy and sell, Communications of the
ACM 42 (3) (1999), (81-ff).
[23] J. Niu, K. Cai, S. Parsons, E. Gerding, P. McBurney, Characterizing effective auction mechanisms: insights from the 2007 TAC Market Design Competition, 7th Int. Conf. on Autonomous Agents and Multiagent Systems (AAMAS08), 2008, pp. 1079–1086.
[24] M. Papazoglou, Agent-oriented technology in support of E-business, Communications of the ACM 44 (4) (2001) 71–77.
67
[25] F. Ren, M. Zhang, Desire-based negotiation in electronic marketplaces, Innovations in Agent-Based Complex Automated Negotiations (2011) 27–47.
[26] F. Ren, K. Sim, M. Zhang, Market-driven agents with uncertain and dynamic outside options, 6th Int. Conf. on, Autonomous Agents and Multi-Agent Systems
(AAMAS07), 2007, pp. 721–723.
[27] F. Ren, M. Zhang, K. Sim, Adaptive conceding strategies for automated trading
agents in dynamic, open markets, Decision Support Systems 46 (3) (2009)
704–716.
[28] C. Sierra, P. Faratin, N. Jennings, A service-oriented negotiation model between
autonomous agents, 8th European Workshop on Modeling Autonomous Agents
in a Multi-Agent World (MAAMAW97), 1997, pp. 17–35.
[29] Y. Tan, W. Thoen, Toward a generic model of trust for electronic commerce, International Journal of Electronic Commerce 5 (2) (2000) 61–74.
Fenghui Ren (www.uow.edu.au/~fren) received his
MCompSc-Res. and Ph.D. from the University of Wollongong
in 2006 and 2010, respectively. He received his BCompSc
from the Xidian University in 2003. Currently, he is the Vice
Chancellor's Fellow in the School of Computer Science and
Software Engineering at the University of Wollongong.
Dr. Ren is an active researcher and published 38 research
papers in reputable journals and conferences. His research
interests include agent-based modeling, simulation, reasoning and learning, agent coordination, negotiation and optimization.
Minjie Zhang is an associate professor in the School of Computer Science and Software Engineering and the Director of
Intelligent System Research Group in the Faculty of Informatics, at the University of Wollongong, Australia. She received a BSc degree from Fudan University, China in 1982,
and her PhD degree from the University of New England,
Australia in 1996. Dr Zhang is an active researcher and published over 130 research papers. She is a program chair for a
number of international workshops and conferences. As a
guest editor, Dr Zhang jointly edited 5 special issues and 6
books. She is the chief investigator for more than 10 different
research grants including an ARC (Australia Research Council) Discovery grant and an ARC Linkage Grants. Her research
interests include multi-agent systems, agent-based simulation and modeling in complex domains, agent-based mart grids and knowledge discovery
and data mining.