Managing commitments in multiple concurrent negotiations
Abstract
Thuc Duong Nguyen a, *, Nicholas R. Jennings b
a MLB1, PP12, B62 Orion Building (B62-MH), Adastral Park, Martlesham Heath, Ipswich IP5 3RE, UK
b School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK
Received 14 April 2005; received in revised form 2 June 2005; accepted 28 June 2005
Available online 22 July 2005
Automated negotiation by software agents is a key enabling technology for agent mediated e-commerce. To this end,
this paper considers an important class of such negotiations – namely those in which an agent engages in multiple concurrent
bilateral negotiations for a good or service. In particular, we consider the situation in which a buyer agent is
looking for a single service provider from a number of available ones in its environment. By bargaining simultaneously
with these providers and interleaving partial agreements that it makes with them, a buyer can reach good deals in an
efficient manner. However, a key problem in such encounters is managing commitments since an agent may want to
make intermediate deals (so that it has a definite agreement) with other agents before it gets to finalize a deal at the
end of the encounter. To do this effectively, however, the agents need to have a flexible model of commitments that
they can reason about in order to determine when to commit and to decommit. This paper provides and evaluates such
a commitment model and integrates it into a concurrent negotiation model.
Ó 2005 Elsevier B.V. All rights reserved.
Keywords: Agents; Automated negotiation; Commitments; Concurrent negotiation
1. Introduction
Electronic Commerce Research and Applications 4 (2005) 362–376
Automated negotiation is a key form of interaction
in agent-based systems and such negotiations
exist in many different forms [1]. In this paper, we
focus on one such form, namely one-to-many
negotiations in service-oriented contexts. Here, a
* Corresponding author.
E-mail addresses: duong.nguyen@bt.com (T.D. Nguyen),
nrj@ecs.soton.ac.uk (N.R. Jennings).
1567-4223/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.elerap.2005.06.005
www.elsevier.com/locate/ecra
service is simply viewed as an abstract representation
of an agentÕs capability. This view is now
widespread in a range of domains that we are targeting
for our work, including the web, the grid,
pervasive computing and e-business [2]. In more
detail, one agent is seeking to provision a single
service (described by multiple attributes, such as
cost, time, quality, etc.) from a number of potential
providers. Traditionally, this type of encounter
is handled via some form of single-sided (reverse)
auction protocol. However, in previous work, we
T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376 363
introduced multiple, concurrent bilateral negotiations
as an alternative [3,4]. Our approach offers
a number of advantages over its more traditional
counterpart (especially in the time-constrained
environments that motivate our work).
First, in most reverse auctions, the buyer is only
allowed to select an agreement from the set proposed
by the sellers. On the other hand, the
buyer in our approach can also send proposals
and counter-proposals. For multi-dimensional
contracts, this two way communication is
important because it allows the buyer to provide
an indication of the areas of the search
space where it would like to see the agreements
lie. Furthermore, the buyer in our approach can
deploy different strategies when bargaining with
different types of providers. This variability
means negotiation can be tailored to the individual
opponents (e.g., some opponents may
be known to be desperate to obtain a deal),
rather than derived implicitly through the
competition of the sellers (as happens in the
traditional auctions). Also, the agreement
reached in one thread can be used to influence
negotiation behavior in other threads. This
gives the buyer additional strategic information
(and hence bargaining power) that can be
exploited to obtain better deals.
Second, the time at which an agreement is
reached in the multiple concurrent negotiation
case can be reduced. For auctions that do not
have deadlines, the end time is indeterminate
which is unacceptable for our time-constrained
domain. In auctions where there is a deadline,
no agreement can be reached before this time.
On the other hand, by using multiple concurrent
negotiations, deals are likely to be available
before the overall deadline and if these are
deemed satisfactory the agent may decide to terminate
other negotiations (perhaps sacrificing
some potential gain) in order to take benefit
from the agreed deal more quickly.
Despite these advantages, however, the negotiation
protocol in our previous approach was somewhat
unrealistic since it was heavily biased in favor
of the buyer. Thus, during the negotiation, the
buyer agent could make a number of intermediate
deals with various sellers (where each such deal is a
temporary agreement with a specific seller). Then,
when its deadline is reached, the buyer selects the
most profitable deal as the final agreement and
declines others. It can operate in this way because
these intermediate deals are assumed to be binding
on the sellers (meaning they are not allowed to
renege from deals once committed) but not on
the buyer. Although these unbreakable commitments
make it easier for the buyer to achieve good
deals, it is highly disadvantageous for the sellers.
Thus, in order to be applicable in realistic negotiation
situations, the model needs to be extended
so that it can deal with situations in which the providers
can also renege from deals. To deal with this
situation, we develop a commitment manager and
an associated reasoning model that enables the
agent to behave in a flexible and efficient manner.
To date, a number of commitment models have
been developed, each with its own advantages and
disadvantages (see Section 4 for more details). We
base our model on the notion of leveled commitment
contracts [5] in which an agent can decommit
(for whatever reason) simply by paying a decommitment
fee to the other agent. In so doing, our
work advances the state of the art in the following
ways. First, it allows the participating agents to be
able to renege from deals whenever they deem
appropriate, simply by paying a decommitment
fee to their counterparts. Since the providers are
no longer forced to be tied to their commitments,
they have greater freedom in their behaviors.
Second, the agents in our model have different
deliberation mechanisms for various penalty
levels, thus, they can flexibly perform in a wide
variety of e-marketplaces. Finally, our commitment
model allows the buyer agent to have a
trade-off between the number of agreements it
makes and their utility values. This capability
helps it to effectively select different commitment
strategies according to its purchasing objectives.
The remainder of the paper is organized as
follows: Section 2 details our new bargaining model
and Section 3 presents the initial experimental
results. Section 4 relates the model to current work
in the field and, finally, Section 5 presents the
conclusions.
364 T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376
2. The negotiation model
The foundation of this work is the concurrent
negotiation model outlined in [4]. Building on this,
the main contribution of this paper is the integration
of the ability to reason about commitment
and decommitment for the intermediate agreements.
Before we can focus on this new ability,
however, we first need to recap the basic architecture
of our model.
In more detail, the agent that wishes to purchase
the service is called the buyer and the agents
that are capable of providing the service are called
the sellers. Service agreements (contracts) are
assumed to be multi-dimensional. The buyer has
a hard deadline tbmax by when it must conclude its
negotiations for the service. This deadline is also
the time when the service will be performed by
the chosen seller. Similarly, each seller a has its
own (private) negotiation deadline tamax. All agents
have their own preferences about the service and
this information is private. Each agent has a range
of strategies (S) that it can adopt 1 and its choice of
strategy is also private information. Each negotiation
thread (bargaining with a particular seller)
follows a Sequential Alternating Protocol [7]
where at each step an agent can either accept the
offer from the opponent, propose its counter-offer,
renege from its commitment or opt out of the
negotiation (typically if its deadline is reached).
In more detail, the model for the buyer agent
consists of three main components: a coordinator,
a number of negotiation threads and a commitment
manager (see Fig. 1). The negotiation threads deal
directly with the various sellers (one per seller) and
are responsible for deciding what counter-offers to
send to them. The coordinator decides the negotiation
strategies for each thread. After each round,
the threads report back their status to the coordi-
1 Given the time-constrained nature of our encounters, the
types of strategy that we consider are the time-dependent family
introduced in [6]. These can be broadly divided into three
classes: the conceder strategy quickly lowers its value until it
reaches its reservation (minimum acceptable) value. The linear
strategy drops to its reservation value in a steady fashion.
Finally, the tough strategy keeps its value until the deadline
approaches and then it rapidly drops to its reservation value.
Coordinator
Commitment
Manager
Buyer Agent
nator. If a thread reaches a deal with a particular
seller, it terminates its negotiation and waits until
the deadline tbmax is reached. The coordinator will
then notify all other negotiation threads of the
new reservation value and it may change the negotiation
strategy for some of them. The commitment
manager, which is newly introduced in this
work, handles any issue that is related to commitment
and decommitment. It is involved when a
thread needs to decide whether or not to accept
a proposed offer (it makes the decision based on
the buyerÕs current commitment and its commitment
strategy; see Section 2.3 for more detail) or
when a seller decides to renege from a committed
deal (it updates its status accordingly). The result
of the commitment manager (either accept or
reject) will be passed through the coordinator for
cross checking with other threads before getting
back to the calling thread. The detailed working
of the three components are described in the
following subsections.
2.1. The coordinator
Thread 1
Thread 2
Thread n
decline
accept
offer
counter-offer
Fig. 1. System architecture.
Seller 1
Seller 2
Seller n
The coordinator is responsible for coordinating
all the negotiation threads and choosing an appropriate
negotiation strategy for each thread. Before
starting a negotiation, the coordinator considers
the available information about the types of the
sellers that are in the environment. In our case,
we consider that seller agents can be of the following
types: conceder (i.e., they are willing to concede
in search for deals) or non-conceder (i.e., they tend
to negotiate in a tough manner). The set of available
agent types is denoted as Atypes: types =
{con, non}. This information is represented as a
probability distribution over the agent types,
which may be based on past experiences, obtained
from a trusted third party, or from a system of
referrals [8]. If no such information is available,
all agents are assumed to have a uniform
distribution.
There are two further sources of information
that aid the coordinatorÕs decision making: the
percentage of success matrix (PS) and the pay off
matrix (PO). The former measures the chance of
having an agreement as the outcome of the negotiation
when the buyer applies a particular strategy
to negotiate with a specific type of the seller. The
latter measures the average utility value of the
agreement reached in similar situations.
Given this information, the coordinator calculates
the probability of the first seller (a randomly
picked agent from those that will be negotiated
with for the service in question) being of a specific
type. Based on this, the agent calculates the
expected utility of applying the various strategies
at its disposal for this particular seller and selects
the one that maximizes this value. Formally, the
expected utility EU(k) for strategy k 2 S is calculated
as
EUðkÞ ¼ X
PSðk; aÞPOðk; aÞPðaÞ; ð1Þ
a2Atypes
T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376 365
where P(a) is the probability that the seller agent is
of type a and PS and PO are the values in the corresponding
matrices, respectively. After finishing
with the first seller, the coordinator uses a Bayesian
update function to update the probability distribution
of the agent types and continues on with
the second seller. This process is repeated until the
coordinator finishes allocating the strategies to all
the negotiation threads (see [4] for more details).
The other task of the coordinator is to classify
the sellers during negotiation and to change the
negotiation strategies for the threads. Specifically,
the buyer attempts to characterize the sellers,
based on the utility value of their proposals, into
the sets Acon, Anon. Thus, at time t: 2< t 6 tbmax,
called the analysis time, the coordinator tries to
determine if a given seller is a conceder or a
non-conceder. In particular, assume U(a,t0 ) is the
utility value of the offer that seller agent a made
at time t0 :(1 6 t0 6 t), according to the buyer
agentÕs preferences. Then seller a is considered a
conceder if 8t0 2½3; tŠ : Uða;t0 Þ Uða;t0 1Þ
Uða;t0 1Þ Uða;t0 > h where h
2Þ
is the threshold value set on concessionary behavior.
If this condition is violated, seller a is considered
a non-conceder.
Now, given the set of strategies S and the set of
classified seller agents As, the coordinator changes
the strategy for each negotiation thread based on
the type of the agent it believes it is negotiating
with. Specifically, for each agent a 2 As, the coordinator
selects the strategy k 2 S that provides the
maximum expected utility and applies it to the
corresponding thread, using Eq. (1), with
Pðj 2 AtypesÞ ¼
1 if a is of type j
0; otherwise.
2.2. The negotiation threads
An individual negotiation thread is responsible
for dealing with an individual seller agent on
behalf of the buyer. Each such thread inherits its
preferences from the buyer agent and has its negotiation
strategy specified by the coordinator. The
structure of a negotiation thread is presented in
Fig. 2. Specifically, each thread is composed of
three subcomponents, namely communication (represented
by the dotted lines), process (represented
by the bold lines) and strategy (represented by
the normal lines). The communication subcomponent
is responsible for communicating with the
Initialize
Got notified
yes
Process the
notification
no
counter-offer
Make offer
and propose
Change the
reservation
value/strategy
Fig. 2. A single negotiation thread.
Report back to
the coordinator
Wait for
reply
withdraw
Terminate
accept
366 T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376
coordinator and the commitment manager. Before
each round, it checks for incoming messages from
the coordinator and if there are any, it passes them
to the process subcomponent. After each round, it
reports the status of the thread back to the coordinator.
The process subcomponent deals with
messages from the communication subcomponent.
This can either be changing the reservation value
or changing the strategy. The strategy subcomponent
is responsible for making offers/counteroffers,
as well as deciding whether or not to accept
the offer made by the seller agent (by cooperating
with the commitment manager).
2.3. The commitment manager
Each time the buyer and a seller a decide to
agree on an intermediate deal with utility value
U(a,t) (according to the buyerÕs preferences), this
deal is binding on both agents. If either of them
decides to break the contract, it has to pay a
decommitment fee (q) to its opponent. This fee is
dynamically calculated as a percentage of the
utility of the deal 2 and is also based on the time
when the contract is broken. 3 To this end, the function
to calculate the decommitment fee at time
t < tbmax is chosen as follows:
qðtÞ ¼Uða; tÞ q 0 þ
t ta
tbmax ta
ðq max
q 0Þ ;
ð2Þ
where ta is the contract time, when the deal is
agreed upon, q0 is the initial penalty (the fee to
pay if the deal is broken at contract time, ta) and
2 Traditionally, there are two ways of calculating the decommitment
fee, namely fixed value (all contracts have the same
fixed decommitment fee that is decided prior to the negotiation)
and percentage of contract value (the fee is defined as a
percentage of the utility value of the contract). It has been
empirically demonstrated that the latter type allows the agents
to be more flexible in deliberating about their behaviors and
enables them to gain a higher utility value than the former [9].
Consequently, we use the percentage of contract value in our
model.
3 This factor is incorporated to discourage the agent from
dropping its commitment towards the end of the negotiation
(where it is more difficult to draft in a replacement). Consequently,
the later an agent decommits, the more it has to pay.
qmax P q0 is the final penalty (the fee if the deal
is broken at execution time, tbmax).
By means of an illustration, consider the following
example. Assume the buyerÕs deadline
ðtbmaxÞ is 10, the initial penalty (q0) is 5% and the
final penalty (q max) is 10%; a deal with the
expected utility value 0.58 was made at time 6.
At time 9, if the buyer wants to decommit, by
(2), it has to pay
9 6
qðtÞ ¼0.58 0.05 þ
10 6
ð0.10 0.05Þ
¼ 0.58 0.0875 ¼ 0.05075.
Since the buyer agent now has to pay a fee every
time it breaks a contract, it cannot simply just agree
on all deals and, later, select the highest value deal
as the final agreement (as it did in the original
version of our model). Thus, when presented with
a potential agreement from a specific seller, the
buyer has to decide whether it should take this deal
or reject it. In some cases, by rejecting this agreement
and, later on, committing to another deal,
the buyer will gain a better utility value (see Section
3 for more details). To capture this, when presented
with a contract /(a) that has utility value of U(a,t)
from seller a at time t, the buyer will accept /(a) as
an intermediate deal (and renege on its current
commitment, if one exists) if all of the following
conditions are satisfied:
1. If it already has a commitment with another
agent a 0 at time t a 0 and this deal has not been
broken, the utility gained by taking this new
offer must be greater than that of the current
deal, after having paid the decommitment fee.
This means U(a,t) >U(a 0 ,ta 0)+q(t).
2. The degree of acceptance (l) for /(a) must be
over a predefined threshold (s). This threshold
specifies how the buyer should accept the offers,
whether it is greedy (tends to accept any possible
deal) or patient (only deals that provide a
certain expected utility value will be accepted).
l is calculated by comparing the utility value
of /(a) with the predicted utility value of the
next set of contracts from other sellers, also
taking into account the relation between the
current time and the buyerÕs deadline. Specifically,
the formula for calculating l is
Uða; tÞ qðtÞ
t
lð/ðaÞÞ ¼
;
maxfU expðai; tÞjai 2 As n ag tbmax
ð3Þ
where q(t) is the decommitment fee that the buyer
has to pay if it has already committed to a deal
with another seller (if it has not, q(t) is considered
to be 0) and Uexp(ai,t) is the predicted utility of the
next proposal from seller ai. The value of Uexp(ai,t)
is calculated as:
U expðai; tÞ ¼Uðai; tÞþ dUðt; t 1Þ
dUðt 1; t 2Þ
jdUðt; t 1Þj;
ð4Þ
where dU(t1,t2) is the distance, in terms of utility
value, between two offers of seller ai at time t1
and t2: dU(t1,t2) =U(ai,t1) U(ai,t2).
To illustrate the operation of the commitment
manager in more detail, consider the following
example. There are 4 participating sellers, the
buyerÕs deadline (tbmax ) is 6, the initial penalty (q 0)
is 10%, the final penalty (qmax) is 20% and the
threshold (s) is 0.8. The buyer has committed on
a deal with seller 4 at time 2 with the expected
utility value of 0.21. The utility values of previous
offers from all the sellers are displayed in Table 1.
At time 3, the buyer has to decide whether it
will accept the offer /(a 3) from seller a 3. Since it
is already committed to a deal with a 4, if it wants
to take /(a3), it will have to pay a decommitment
fee to a4. By(2), the fee it has to pay is
3 2
qð3Þ ¼0.21 0.1 þ
6 2
T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376 367
ð0.2 0.1Þ ¼ 0.026.
As can be seen, U(a 3,3) < U(a 4,2) + q(3), so the
first condition is violated. Thus, the buyer will
reject /(a3) and remain with its commitment with
a4.
Table 1
Utility values of the offers
Agent t =1 t =2 t =3
a1 0.03 0.12 0.16
a 2 0.01 0.04 0.10
a3 0.1 0.19 0.23
a4 0.11 0.21 –
At time 4, however, seller a4 decides to renege
on its current deal and pay the decommitment
fee to the buyer. According to Eq. (2), it has to pay
4 2
qð4Þ ¼0.21 0.1 þ
6 2
ð0.2 0.1Þ ¼ 0.0315.
As can be seen, this decommitment from a4
leaves the buyer with no agreement. Now, at time
5, the buyer has to decide if it should take up the
offer from a 1 (Table 2 shows the utility values of
the offers from all the sellers). Since it has no intermediate
agreement, the first condition is satisfied.
To evaluate the second condition, the buyer first
calculates the value for Uexp(a1,5) and Uexp(a2,5)
using (4):
U expða2; 5Þ ¼0.26 þ 0.04
0.2
0.04 ¼ 0.252;
U expða3; 5Þ ¼0.36 þ 0.05
0.08
0.05 ¼ 0.391.
The value of l(/(a1)) is then calculated, using Eq.
(3), as
lð/ða1ÞÞ ¼ 0.4
0.391
5
¼ 0.852.
6
This time, since l(/(a1)) > s, the buyer will commit
to this deal. It keeps on bargaining in this way
until its deadline is reached. If, at that time, there
is an intermediate deal that has not been broken,
this deal is selected as the final agreement. If,
however, no such deal exists, the negotiation is
considered unsuccessful and terminated without
an agreement.
Up until this point, we have only considered the
situation where the buyer agent commits to a
maximum of one intermediate contract at one
time. However, it possible for the buyer to commit
to more than one contract at any one time and
then, later, select the best one and decommit from
the others. This represents a cautious approach
Table 2
Utility values of the offers (cont.)
Agent t =1 t =2 t =3 t =4 t =5
a1 0.03 0.12 0.16 0.28 0.4
a 2 0.01 0.04 0.10 0.30 0.26
a3 0.1 0.19 0.23 0.31 0.36
a4 0.11 0.21 – – –
368 T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376
and avoids the risks associated with committing to
only one contract which is then revoked near the
deadline, leaving the agent with insufficient time
to find a replacement. The downside of this
approach, however, is that if the sellers do not
renege, the buyer may end up paying a significant
part of its utility value as the penalty fee. Nevertheless,
in some cases, it may be beneficial for the
buyer to consider the option of having multiple
commitments during the bargaining process. To
capture this, assume that the maximum number
of commitments that the buyer will hold at any
one time is x P 1 and let X ={Ci|i 2 [1,x]} be
the set of contracts that the buyer is currently
committed to: |X| 6 x. Here, Ci ={/ 0 ,t0 } is the
contract that consists of an intermediate deal / 0
that has been agreed at time t0 . Assuming that at
time t, there is an offer / from seller k that has
l(/(k)) > s (see Eq. (3)) 4 and U(/(k),t)>U(/ 0 ,
tk0)+q(t) "C(/0 ,tk0) 2 X then this offer will then
be accepted by the buyer. This, in turn, means
the following steps will be taken:
1. If X is not full (i.e., |X| <x), C(/,t) will be
added to X: X = X\C(/,t).
2. If X is full (i.e., |X| =x) select C(/ 0 ,tk0) 2 X
that has the minimum value of U(/ 0 ,tk0) and
decommit from that contract. Then, C(/,t) will
be added to X: X = X\C(/,t).
Now if a seller k that has a contract C(/(k),t k)
decides to withdraw its commitment, that contract
will be subtracted from X: X = XnC(/(k),tk).
Then at the end of the bargaining process, if there
is more than one contract in X, the buyer simply
selects the one that has the highest utility value
as the final agreement and decommits from all
the others.
3. Empirical evaluation
Having introduced the commitment manager,
the next step is to evaluate its effects on the model.
4 If |X| <x, q(t) is considered to be 0. If not, q(t) is the
penalty the buyer will have to pay to break from the contract
C(/ 0 ,tk 0) 2 X that has the minimum value of U(/0 ,tk 0).
We choose empirical evaluation as the method of
measurement for a number of reasons. First,
because our model is heuristic in nature, it is difficult
to make meaningful theoretical predictions.
Second, there are a number of internal variables
that control the behavior of the model, as well as
external variables that define the environment in
which the model is being used. These variables
are interrelated and need to be considered in a
broad range of situations. Empirical techniques
allow us to manipulate these variables, conduct
the experiments and analyze the results.
3.1. Experimental setup
In more detail, we use the exploratory studies
evaluation technique [10]. With this method,
general hypotheses are formed to express the
intuitions about the causal factors within the
model. The experiments are then conducted and
generate the results that either support these
hypotheses or go against them. In our evaluation,
the independent variables are given in Table 3 and
the dependent ones are listed in Table 4.
Apart from the control variables described in
Table 3, other control variables are selected as
per [11]. Specifically, the number of seller agents
(n) is set in the range of [1, 30] and the number of
negotiation issues (m) is set in the range of [1, 8].
An agent aÕs preference for issue j is represented
by the tuple fx a j min ; x a j max ; w a j g. The tuple ½xa j min ; x a j max Š
Table 3
The independent variables
Variables Descriptions Values
q0 The initial penalty fee [5,100]
qmax The final penalty fee (qmax P q0) [5,100]
s The l threshold [0,1.5]
x The number of concurrent commitments [1,4]
Table 4
The dependent variables
Variables Descriptions
U The utility value of the final agreement
N The number of successful negotiations
D The number of decommitments made by buyer
T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376 369
is an interval independent variable, whose scale is
infinite. To simplify the analysis, therefore, we
assume all issues have the same domain of values
and we randomly set the value for xa j to be in
min
the interval [0, 20] and xa j to be in the interval
max
[30, 50]. The values for wa j are set to give all issues
equal importance. The negotiation deadline for
each agent is an ordinal independent variable,
whose value is randomly chosen, ranging from 5
(very short deadline) to 50 (long deadline). The
penalty fee (both initial and final) is also an ordinal
independent variable, whose value is randomly
chosen, ranging from 5% (small) to 100% (equal
to the value of the contract). Similarly, the s threshold
is either 0 (meaning the buyer is greedy and will
commit to any intermediate deal that it can get
hold of) or 0.5 (meaning the buyer is patient and
will only engage on a deal that provides high
expected utility value). 5
The seller agents in this evaluation are characterized
in a similar fashion to ones set up in our
previous experiments [4]. Specifically, they are
characterized by three independent variables
whose values are set in the following manner:
The valuesÕ domain for the set of negotiation
issues: These domains are randomly generated
(from the same distribution as the buyer agentsÕ
values) so that each domain intersects with the
corresponding domain of the buyerÕs preference.
For example, if the buyerÕs value domain for an
issue j is ½x b j min ; x b j max Š then the corresponding value
domain for seller a will be generated as ½x a j min ; x a j max Š
that satisfies x b j min 6 x a j min 6 x b j max 6 x a j max .
The negotiation strategy: Each seller is assigned
a random strategy selected from a predefined
set of alternations (as outlined in [6]). This set
is composed of time-dependant functions (like
conceder, boulware and linear) and behaviordependant
tactics (such as tit-for-tat in its various
forms).
The negotiation deadline: The deadline for each
seller is generated from the same distribution as
for the buyer.
5
Future work will investigate in more detail how this value
affects the outcome of the model.
The only difference is that now if a seller has
committed to a deal, it has a chance of being made
an outside offer with the utility value of 1.0 (which
is the highest possible utility value). Thus, there is
a probability that it will decommit. To this end, we
consider three types of sellers:
Loyal: once a seller has committed to an intermediate
deal, it will not renege from it.
Loose: a seller always breaks a committed deal
if it is presented with a better option.
Partial: if a seller finds a better option, it will
break a committed deal with a percentage of
probability (as per [12]). In this experiment,
we set this percentage to be 50%, meaning that
half of the time a seller finds a better deal, it will
renege and half of the time it will stay with its
current deal.
After each experiment, we measure the utility
value of the final agreement for the buyer (U). In
our evaluation, the utility of an offer X =
{x 1,x 2,...,x m} to an agent a is calculated as
UðX Þ¼ Xm
j¼1
w a
j
xj xa jmin xa jmax xa jmin We also measure the number of agreements
reached at the end of the negotiation encounter
(N) and the average number of decommitments
that the buyer made (D). In all cases, the results
are gathered from a series of experiments in different
environment settings. Each experiment consists
of 1000 runs and the results are averaged and put
through a regression test to ensure that all differences
are significant at the 99% confidence level.
3.2. Experimental hypotheses
We now turn to the specific hypotheses.
Hypothesis 1. When dealing with loose or partial
sellers, the higher the penalty fee is, the lower the
number of final agreements reached by the buyer.
To evaluate this hypothesis, we measure the
number of final agreements achieved with varying
types of seller agents (see Fig. 3). As can be seen,
the number of final agreements reached by the
.
370 T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376
Fig. 3. Number of successful negotiations for varying penalty
fee.
buyer is dramatically reduced as the penalty fee is
increased. Specifically, when dealing with loose
sellers, around 97% of the negotiations are successful
when the penalty fee is 5%. As the penalty fee
increases to 100%, this success rate drops down
to only 84%. Similarly, the figures when dealing
with partial sellers are 98% and 92%, respectively.
This decreasing trend is explained by the deliberation
mechanism of the buyer. Specifically, assume
that the buyer has already made a commitment
with seller k and now it is presented with another
offer from seller k 0 . If it decides to take this new
offer from k 0 , it will have to pay k a decommitment
fee q. As the penalty fee is increased, so is q. Thus,
in some cases, the buyer cannot afford to take this
new offer and it has to stay with its commitment to
k. Later on, if k decides to break its commitment,
the buyer is left with no intermediate agreement.
As such, there may not be enough time for the
buyer to find another replacement deal and, thus,
no final agreement can be reached. On the other
hand, if the buyer can take the offer from k 0 , the
probability that k 0 will renege is less than that of
k. Thus, a final agreement can be reached.
Another observation is that the more loyal the
seller is, the greater the number of final agreements
that the buyer makes. This difference is caused by
the probability of the sellers breaking their
commitments. Since a loyal seller never reneges,
once it has committed, its contract is kept until
either it is declined by the buyer or it is selected
as the final agreement. Therefore, once an intermediate
deal is reached, a final agreement is always
guaranteed to exist. However, this is not the case
for the other types of sellers. Once they have committed,
it is not guaranteed that they will actually
stay faithful with their commitments. If a seller
breaks a contract, the buyer has to find a replacement.
If it fails to do so, no final agreement will be
achieved. Thus, the less loyal the sellers are, the
fewer chances there are for the buyer to reach a
final agreement.
Hypothesis 2. The higher the penalty fee, the
lower the utility of the final agreement gained by
the buyer.
As can be seen from Fig. 4, this trend is true for
all seller types. Specifically, when dealing with
loose sellers, the average utility of the final agreement
for the buyer drops from 0.61 to 0.46 when
the penalty fee goes from 5% to 100%. The corresponding
figures for partial and loyal sellers are
0.62–0.43 and 0.63–0.40, respectively. The reason
for this decrease in the final utility value is that
the higher penalty fees mean more chance that
the buyer will commit to an early agreement (and
stay with this commitment until either its deadline
is reached or the corresponding seller decides to
renege). These early commitments by the buyer
have two main effects. First, such agreements tend
to have lower utility value for the buyer, compared
to the contracts that are offered at a later stage (the
buyer cannot afford to take these contracts due to
Fig. 4. Final utility value for varying penalty fee.
T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376 371
high decommitment fees). Second, once that commitment
is later broken, the buyer will have to find
a replacement. Even if it is successful in finding
one, since there is not much time for bargaining,
the utility value of this newly found agreement is
likely to be less than that of the previous deal.
Consequently, the utility gained by the buyer is
reduced.
Furthermore, with increasing penalty fee, the
more loyal the seller, the lower the value of the
final agreement gained by the buyer (see Fig. 4).
The reason for this observation is because the
buyer benefits from the decommitment fee gained
when a seller reneges from a committed deal. As
per our experimental setup, loose sellers decommit
more often than partial sellers and loyal sellers
never renege. Thus, as the penalty fee increases,
the buyer will benefit more when dealing with less
loyal sellers.
Hypothesis 3. The buyer decommits less frequently
as the penalty fee increases.
Fig. 5 shows the average number of decommitments
made by the buyer for varying penalty fees
and different seller types. Since the buyerÕs deliberation
includes the decommitment fee it has to pay
if it want to replace its current intermediate deal
(see Eq. (2)), the less it has to pay, the more favorable
it will be to take up a better deal. Thus, even
when a seller offers an intrinsically higher value
contract than the current deal it has, the buyer
ρ ρ
may be better off sticking with its existing commitment
in order to avoid paying a hefty fine. This is
why the buyer almost never reneges when the
penalty fee is close to 100%.
Hypothesis 4. The more patient the buyer, the
higher the utility for the final agreement. However,
the chance of having a final agreement is reduced.
We start by looking at the performance of the
model with a number of different values for the
degree of acceptance (specifically s2[0.1,1.5]). For
simplicity, we fix the penalty fee value at (q0 =5,
qmax = 10) and assume we are dealing with partial
sellers. These values are chosen just to give us an
idea of how the results could potentially be and a
detailed analysis will follow. The results are displayed
in Fig. 6.
As can be seen, as the value of s increases, the
utility value for the final agreement decreases. This
is because in a particular negotiation, if the buyer
tends to ignore the current offer from the seller, in
favor of a higher value one at a later time, there is
a possibility that a high value offer will not be
forthcoming (e.g., the seller may run out of time
or be at the limit of its reservation values). Thus,
towards the end of the encounter it will have to
settle for a lower value deal (because this is better
than no deal). This, in turn, puts a downward
trend on the final utility value achieved.
On the other hand, the number of final agreements
reached increases as the value of s increases
up to 0.5, then it decreases. Now, since we are
Fig. 5. Number of buyerÕs decommitments for varying penalty
fee. Fig. 6. Performance vs. degree of acceptance.
372 T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376
dealing with partial sellers, if they are presented
with a better outside offer, they have the chance
to renege and may leave the buyer with no agreement
at hand. When the value for s is small (less
than 0.5 in this case), the buyer tends to take up
any offers that are available to it at an early time.
Later, when the seller that is sharing the commitment
with the buyer decides to back down, there
might not be enough time for the buyer to recover
from this loss and, thus, it might end up with no
agreement at the end of the encounter. However,
if it is too strict on accepting intermediate deals,
it also risks the chance of having obtained no deal
at all. This is the situation when the value of s
increases past 0.5. From Fig. 6, it can be seen that
by setting value of s at around 0.5, the buyer will
achieve the highest number of final agreements
with a reasonably good final utility value.
We extend the aforementioned result by comparing
the results of having two different values
for s: greedy (s = 0) and patient (s = 0.5) in the
experiments with different penalty values, as well
as different seller types. Recall, the greedy buyer
will commit to any offer that it can take (if it is
more beneficial than the one it currently has, taking
into account the decommitment fee it will have
to pay). In contrast, the patient buyer will only
commit to an offer that has significantly greater
value (compared with the one that it currently
has). As it only accepts higher value contracts
compared to its counterpart, the patient agentsÕ
final agreements always have higher utility value
than those of the greedy agent (see Fig. 7).
Now, not only does the patient agent gain higher
utility value, the number of successful agreements
achieved is also higher than or, at least, equal to
that of the greedy agent (see Fig. 8). The reason
for this is related to the way an intermediate agreement
is accepted by the buyer. The greedy buyer
accepts a higher number of intermediate agreements
than its counterpart. 6 Thus, its chance of
having an agreement reneged upon is higher than
that of the patient agent. In some cases, this decommitment
limits the chance of the buyer of having an
6 The greedy buyer accepts any possible agreement, whereas
the patient one only accepts agreements that have a significantly
greater value compared with the one that it currently has.
Fig. 7. Final utility value for varying penalty fee.
Fig. 8. Number of successful negotiations for varying penalty
fee.
agreement at the end of the negotiation. Consequently,
the patient agent will be able to reach
more agreements than the greedy one at the end
of the bargaining process.
However, even though it can gain better utility
value than its greedy counterpart, the patient agent
manages to get fewer agreements than its counterpart.
This is because the patient agent only accepts
a deal if the degree of acceptance (l) of this deal is
greater than a threshold (in this case, s = 0.5).
Thus, not all the deals proposed by the sellers
satisfy this condition. Indeed, in some cases, none
of the proposed contracts satisfy this condition.
This limits the chance of the buyer having an
agreement at the end of the negotiation. On the
T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376 373
other hand, the greedier the agent is, the higher the
chance that an offer will be accepted. Consequently,
the greedy agent will be able to reach
more agreements than the patient one at the end
of the bargaining process.
Hypothesis 5. When dealing with loyal sellers, the
buyer is better off committing to a maximum of
one contract at any one time. For other seller
types, the buyer should commit to a maximum of
two contracts.
Fig. 9 shows the number of agreements obtained
by the buyer at the end of the encounter when it
varies the number of commitments it can hold at
any one time (here x 2 [1, 4]). As can be seen, when
holding more than one commitment, the buyer
increases its chance of reaching an agreement when
dealing with non-loyal sellers. In particular, when
x is increased from 1 to 2, the buyer gains 0.9%
more final agreements when dealing with partial
sellers and 2% more when dealing with loose sellers.
This improvement can be explained simply
by looking at the behaviors of the sellers. As the
sellers are not loyal, when presented with an outside
offer, they may renege. If this happens near
the end of the negotiation process and the buyer
can only commit to a single contract, it will leave
the buyer very little time to find an alternative
(and in some cases it will not be able to do so).
On the other hand, if the buyer is holding more
than one contract and an agent reneges then it
has something that it can fall back on and it is less
vulnerable to being left with no agreement. For
values of x > 2, however, the improvement is
comparatively minor because when the buyer is
committing to more than one contract, the chance
that all the sellers renege is significantly reduced
compared to the situation when the buyer can only
have one commitment at a time. This, in turn, has a
very slight impact on the number of agreements
achieved.
The final utility achieved by the buyer with
varying values for x is displayed in Fig. 10. As
can be seen, when x > 2, the utility gained is dramatically
reduced (8% decrease when x goes from
2 to 3 and 16% decrease when x goes from 3 to 4).
This is because if a buyer agent has more contracts
at the end of the negotiation process, it will end up
paying a significant penalty fee for breaking them.
When x = 2, the situation is similar to that of
dealing with loyal sellers. However, when negotiating
with partial or loose sellers, x = 2 gives similar
results and, in some cases, is better than setting x
to 1. The reason for this is because as the non-loyal
seller agents can renege on their commitments and
if they do so towards the end of the negotiation
process, the buyer will gain additional penalty fees
from those sellers and is still left with at least one
intermediate contract in hand. Thus, at the end, it
is still able to have the final agreement, but it does
not have to pay a decommitment fee to any other
seller agent.
Fig. 9. Number of agreements vs. buyerÕs maximum commitments.
Fig. 10. Final utility value vs. buyerÕs maximum commitments.
374 T.D. Nguyen, N.R. Jennings / Electronic Commerce Research and Applications 4 (2005) 362–376
As can be seen, when dealing with loyal sellers,
the buyer does not necessarily need to have more
than one commitment since it can be sure that
the sellers will never renege from their deals. However,
when dealing with partial or loose sellers, the
situation is different. The greater the number of
commitments it holds, the higher the number of
final agreements it is likely to obtain. Nevertheless,
the final utility value reached is decreased because
it will have to pay a large amount of penalty fees to
decommit from these commitments. To this end,
the buyer is best setting x to 1 when dealing with
loyal sellers and x to 2 when dealing with other
types of seller to ensure that it will achieve highest
possible utility value together with an acceptable
number of final agreements.
4. Related work
Traditionally, once a contract is made in a negotiation,
it is binding on all participants. Neither
party can back out no matter what happens in
the future [13–15]. This is also the case for existing
concurrent negotiation models [4,16,17]. However,
this view is very limiting for the agents and it may
lead to irrational and inefficient behavior [12].Asa
result, a number of methods have been developed
to overcome this limitation.
One of the first pieces of work in this area was
the contract net protocol [18], where there is a possibility
for a decommitment. Here, the contracter
agent could send a termination message to cancel
the contract, even when a part of it has been fulfilled
by the contractee. As the agents participating
in a contract net are generally assumed to be cooperative,
they do not mind losing their effort (even
without any form of compensation). In a similar
fashion, the role of commitment for cooperative
agents was examined in the context of automated
scheduling of meetings [19]. In e-commerce settings,
however, these models are inappropriate
because the agents are not always cooperative
and they seek to maximize their individual gains.
For self-interested agents, contingency contracts
have been introduced as a method of allowing
them to break commitments [20]. In this case, an
agentÕs commitment to a contract is made contin-
gent on specific future events. Thus, if these specified
contingencies aries, the agents are allowed to
drop their commitments [21]. However, there are
a number of problems associated with this type
of contract [5]. First, not all possible future events
are known to the agents beforehand, thus, they
cannot always make optimal use of contingency
contracts. Second, this type of contract is useful
when the number of future events is small. If, however,
this number increases, it is cumbersome or
even impossible for all the events to be monitored.
Furthermore, these events may not affect the original
contract independently, they may have a combined
effect on the value of the contract [13]. Asa
result, this approach is not adopted in our work.
The most advanced work in the area, and also
the basis to our work, is the leveled commitment
contracts (LVC) [5]. Our commitment manager is
built upon the same basic intuition that any agent
can freely decommit from a contract, for whatever
reason they deem appropriate, by simply paying a
decommitment fee to the other partner. However,
our model is different in a number of important
ways. First, the original LVC only covers a two
person game. We have extended this to cover the
multiple providers found in our target environment.
Second, we do not just reason about decommitment,
we also deliberate about when and how
to make a commitment. Third, LVC require the
agents to have information about the actual and
alternative options of their opponents in order to
be able to calculate the Nash equilibrium decommitment
threshold. This assumption is unrealistic
in practical scenarios and is not required in our
model. Finally, unlike LVC (which typically
assumes a fixed penalty for decommitting, regardless
of the stage of the process at which the
commitment is broken), our model takes the cost
of ongoing commitment into account by introducing
variable penalty contracts. Again, we believe
this is more realistic for most real-world settings.
5. Conclusions and future work
This paper has introduced a commitment
handling capability that can be applied in managing
concurrent negotiations in time-constrained
settings. This ability increases the flexibility and
realism of the participating sellers and relaxes the
previous unrealistic constraints we imposed [3,4].
Our empirical results have highlighted the fact that
different penalty levels have different effects on the
performance of the model. In addition, we show
that the more patient the buyer is, the better the
deal it will obtain. Nevertheless, if the buyer wants
to secure more agreements, it should be greedier in
making commitments. Our extended model is also
currently being used in a number of real world
applications to form and maintain coalitions in
business and e-science virtual organizations [22]
and in an internal project of BT concerned with
logistics planning [23].
For the future, there are a number of ways in
which our model can be improved. First, we would
like to experiment with different strategies (e.g.,
alternative methods for the buyer to decide
whether or not to accept an offer from a seller)
for our buyer agent to see how they affect the final
outcome of the model. Second, we would like to
investigate different penalty levels for different
agents, perhaps based on their negotiation histories.
In particular, if an agent comes to the negotiation
with poor reputation (e.g., it frequently
reneged on its previous encounters), that agent
should have to pay a higher penalty fee than one
that has shown itself to be more trustworthy.
Finally, we would like to improve the decision
making of our agents so that they can make more
accurate predictions about their opponentsÕ
decommitment strategies. This will, we believe,
also increase the performance of the model.
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