DESIGN AND EVALUATION OF AGENT-BASED
NEGOTIATION HEURISTIC FOR ONLINE NEGOTIATIONS
Kaushal Chari, Manish Agrawal
University of South Florida, 4202 E Fowler Avenue, CIS 1040, Tampa, FL 33620-7800, USA
Ke
ywords: Software agents, electronic markets, automated negotiations.
Abstract: This paper presents a negotiation heuristic for software agents that enable agents to learn about the
opponent’s behavior and use market information while conducting online negotiations. The heuristic is
tested in a pilot experimental study, where the performance of agents is evaluated with respect to human
negotiators in a simulated electronic market. Preliminary results indicate that agents may have the potential
to do better than humans in multi-issue negotiation settings.
1 INTRODUCTION
Software agents (Chari and Seshadri 2004) have the
potential to act as effective surrogates of their
human principals during automated negotiations due
to their ability to overcome the cognitive and
information processing limitations of humans in
negotiation tasks. Although many research
prototypes have been developed to enable software
agents to negotiate (see Section 2), to our
knowledge, they all suffer from some weaknesses as
pointed out in Section 2. In the quest for developing
software agents that are more robust and effective
for online negotiations, we propose a learning
heuristic for software agents, implement this
heuristic in a multi-issue negotiation setting (i.e., an
electronic marketplace), and evaluate its
effectiveness compared to humans using a pilot
experimental study.
The context of agent-based negotiations is an
electronic marketplace with a finite open time
window for completing transactions. Buyer and
seller agents register in the e-marketplace and
transact a given quantity of an item within the
predefined time window. Both buyer and sellers are
cognizant of the market values and use this
information during negotiations. An agent can
negotiate with multiple opponents sequentially to
transact the required quantity, since a single seller
for example, may not be able to meet the entire
demand of a buyer agent. These conditions are
similar to trading in a commodity exchange
(Chicago Board of Trade 1998). A transaction is
completed successfully when an agreement is
reached on all issues under consideration such as
price, delivery terms, etc. The preference structure
of human principals are elicited and stored in their
surrogate agents as utility functions. The agents
negotiate on behalf of their principal until either an
agreement is reached or the time window expires.
2 LITERATURE REVIEW
Business negotiations have been studied from
various perspectives including game theory,
economic, socio-psychological, and intelligent
approaches. Game theoretic approaches make fairly
restrictive assumptions about opponent behaviors,
thereby rendering them somewhat impractical in
real-life negotiation settings (
Kraus and Wilkenfeld
1993).
Economic approaches (Zeuthen 1968) treat
negotiations as a finite sequence of offers and
counter offers that could converge to an agreement
if an agreement zone exists, deriving subsequent
offers based on expectations about the opponent’s
behavior. Intelligent approaches, based on artificial
intelligence and/or statistical techniques, can
facilitate learning of an opponent’s behavior,
provide efficient search of the negotiations solution
space for an agreeable solution, and automate the
negotiations process. Examples of intelligent
approaches include case-based reasoning, heuristic-
searches, automated learning, Bayesian techniques,
92
Chari K. and Agrawal M. (2004).
DESIGN AND EVALUATION OF AGENT-BASED NEGOTIATION HEURISTIC FOR ONLINE NEGOTIATIONS.
In Proceedings of the Sixth International Conference on Enterprise Information Systems, pages 92-97
DOI: 10.5220/0002604500920097
Copyright
c
 SciTePress

and genetic algorithms. Case-based approaches,
which match previous recorded instances of
negotiations from the case history to the current
situation (e.g., PERSUADER system (
Sycara 1990)),
are not effective when existing cases in the case
history database do not match the current
negotiation situation. Genetic algorithms pit one
negotiation strategy against another, and use the
outcome to produce improved strategies from
subsequent generations in an evolutionary manner
(
Oliver 1996). However, they often require a very
large number of generations to refine the negotiation
strategy. Heuristic techniques search a multi-
dimensional space for a point that is agreeable to all
negotiating entities. Bayesian approaches provide
the ability to learn during negotiations using
probability update rules (
Zeng and Sycara 1998);
however, such probabilities are difficult to define ex
ante and may sometimes be inaccurate.
Many agent systems have been developed for
automated/semi-automated negotiations. One of the
pioneering systems is the Kasbah agent system,
which uses a simple negotiation heuristics based on
pre-defined price decay or increment functions
(
Chavez and Maes, 1996). Kasbah agents do not learn
and therefore do not adapt to the negotiation
environment. Agents developed in the Bazaar
project (
Zeng and Sycara 1998) use Bayesian update
rules to learn and form beliefs about the opponent’s
behavior. As stated before, this approach is limited
by the difficulty in assessing various probabilities
used in Bayesian update rules. Faratin et al. (1998)
use families of polynomial and exponential
functions to model opponent concession behaviors
during negotiations (e.g., boulware, conceder and
imitative behaviors) and combine them using
weights to create a negotiation strategy. This
approach requires human intervention to assign
weights for alternative negotiation strategies and
does not provide agents with any learning
capabilities. Chari and Bhattacherjee (2002) present
a heuristic for agent negotiations that learns from
the opponent’s behavior. However, this heuristic
suffers from unrealistic requirements such as the
need for agents to know the market demand supply
ratio, and the lack of robustness for various
negotiation settings.
The review of the above literature indicates
that: 1) there is no research prototype that is
intelligent and robust enough to support automated
negotiations in real world negotiation settings, and
2) No research has investigated the performance of
existing agents with respect to humans in live e-
marketplace negotiations. The current research aims
to address these limitations by building a learning-
based negotiation heuristic that uses market values
in determining bids in real time. We also present
results of a pilot experimental study that compares
the performance of agents with humans.
3 NEGOTIATION HEURISTIC
A negotiation heuristic determines the scheme for
making offers/bids (hence forth referred to as simply
offers) during negotiations. Negotiations involving
multiple issues (such as price, financing rate,
delivery term etc) require the two negotiation
partners to agree on all the issues. We present a
negotiation heuristic that supports multiple issue
negotiations. This heuristic uses the utility function
as well as the reservation values of various issues
while making offers. The utility functions are
generated by eliciting preferences from the human
principal of an agent. The heuristic learns from the
opponent’s behavior, uses market conditions in
making offers and handles multiple threads
sequentially within a limited time window. We
make the following assumptions: (a) bilateral
negotiations; (b) the negotiators are always in
conflict over each issue; (c) the utility value of an
offer for any issue never exceeds the utility value of
an earlier offer for that issue.
The central idea behind the heuristic is as
follows. An agent implementing the heuristic
estimates the number of iterations required to reach
the market value by estimating the opponent’s
concession curve by fitting the best curve on the
opponent’s observed offer points. Using this
information as well as information on market
values, the agent estimates the target value that it
should strive to reach at the last iteration of the
negotiations thread. The agent then determines the
concession rate to move from its last offer to the
target offer for an issue in the remaining iterations
and then accordingly makes an offer subject to some
constraints. Notations used in the heuristic are
given in Table 1.
Before an agent enters into negotiations with an
opponent, its human principal provides: (a) a bound
on the maximum number of iterations for that
thread, tmax
is
, (b) own reservation values, and c)
starting bid values for all issues.
DESIGN AND EVALUATION OF AGENT-BASED NEGOTIATION HEURISTIC FOR ONLINE NEGOTIATIONS
93

Table1: Notations used in negotiation heuristic
Symbol Description
y
lk
Market value of issue k, i.e., value of k for last the successful transaction in the marketplace.
x
ij
= [x
ij1
,,…,x
ijn
] is the vector of n issue values proposed by agent i at iteration j.
Tmax
i
Total time available to agent i for negotiations. Typically the length of the time window of the
market place.
u
i
(x
1
,..,x
n
) Utility function of agent i as a function of n issue values.
Q
i
Quantity required to be transacted by agent i during Tmax
i
r
i
=[r
i1
,…, r
in
] reservation value vector of agent i containing reservation values for n issues.
τ
ij
= [
τ
ij1
,…, τ
ijn
] is the vector of target values of n issues for agent i at iteration j, that agent i
strives to achieve as the agreed solution.
cr
ij
= [cr
ij1,…,
cr
ijn
] is the vector of concession rates of agent i at iteration j across n issue
dimensions.
s
ij
= [s
ij1,…,
s
ijn
] is the vector of step sizes of agent i at iteration j across the n issue dimensions.
t
ijk
Number of additional iterations estimated by agent i at iteration j for issue k in the current
thread.
mn
jk
Estimate at iteration j of the minimum value for issue k that the opponent uses in making
offers. This value is used in (1).
mx
jk
Estimate at iteration j of the maximum value for issue k that the opponent uses in making
offers. This value is used in (1).
tmax
is
Bound on the maximum number of iterations of agent i in thread s. tmax
is
≥ j + max
k
(t
ijk
).
q
s
Quantity transacted during negotiation thread s when an agreement is reached with the
opponent.
I
i
Set of negotiation issues such that the utility value of agent i is non-decreasing with respect to
increasing issue values. For example, interest free payment period in case of a buyer.
D
i
Set of negotiation issues such that the utility value of agent i is non-increasing with respect to
increasing issue values. For example, price in case of a buyer.
δ
I
Constant between 0 and 1 that denotes the fraction of the market value that could be reduced
from (denoted by index i = 1), or added to (denoted by index i = 2), the market value in
determining the settlement target.
round(x) Rounds x to the nearest value in the domain of x.
The opponent’s maximum number of iterations for a
given thread is estimated by learning from the
opponent’s behavior. We use the exponential
function proposed in (
Faratin et. al. 1998) to model
the entire range of concession behaviors of the
opponent. According to this function, the
opponent’s offer at iteration j for issue k can be
computed by (1) as follows.
x
ojk
={mn
jk
+ α
jk
.(mx
jk
– mn
jk
) for k ∈ D
o
(i.e., I
i
)
mn
jk
+(1- α
jk
)(mx
jk
– mn
jk
) for k ∈ I
o
(i.e., D
i
)
where
α
jk
= exp((1 – min(j, tmax
k
)/tmax
k
) β
jk
ln k
jk
),
β
jk
> 0 and 0 < k
jk
< 1 (1)
In (1) the parameter
β
jk
captures the type of
negotiations behavior: boulware (
β
jk
<1), conceeder
(
β
jk
> 1) etc; k
jk
is the estimate at the j
th
iteration for
the starting value of
α
jk
. While parameters β
jk
, t
maxk
,
mn
jk
(for k ∈ I
o
), mx
jk
(for k ∈ D
o
) and k
jk
can be
estimated by fitting a curve through opponent’s
observed offer points till iteration j: x
o1k
,…, x
ojk
,
while minimizing the least squared error, only
parameter t
maxk
is used by the heuristic. Note that the
reservation value of opponent can be estimated from
parameters mn
jk
(for k ∈ I
o
), mx
jk
(for k ∈ D
o
),
however the agent uses the market value instead of
the opponent’s reservation value estimates in
making bids. The estimate of the number of
additional iterations at iteration j to reach an
agreement on issue k is given by (2). Note that the
total number of iterations in a thread is subject to the
bound set by the user of the agent.
t
ijk
=max( min( tmax
k
, tmax
is
) – j, 1) (2)
A target value is computed for each issue based
on the market conditions according to (3). This is
the value at which agent i, strives to reach an
agreement.
τ
ijk
= min(max ((1- δ
1
)y
lk
, r
ik
), x
ij
-1
k
) for k ∈ I
i
;
max(min((1+
δ
2
)y
lk
, r
ik
), x
ij
-1
k
) for k ∈ D
i
(3)
For example, when
δ
2
= 0.05, and issue k is
price, then target is set to 105% of the current
market value for price, subject to bounds set by own
reservation price and previous offer made. The
target value is approached at a rate given by the
concession rate in (4).
ICEIS 2004 - SOFTWARE AGENTS AND INTERNET COMPUTING
94

cr
ijk
= ( τ
ijk
– x
ij
-1
k
)/ t
ijk
(4)
The concession rate is then used to compute the
step size for the move from the previous offer as:
s
ijk
= cr
ijk
∆
j
(5)
Note that
∆
j
=1. Agent i’s offer can then be
computed as follows:
x
ijk
=
{max(min (round(x
ij
-1
k
+ s
ijk
), x
ij
-1
k
), τ
ijk
, r
ik
,
x
ojk
) for k ∈ Ii ;
min(max(round(x
ij
-1
k
+ s
ijk
), x
ij
-1
k
), τ
ijk
, r
ik
, x
ojk
)
for k
∈ D
i
} (6)
To reduce the computation time for estimating
the opponent’s concession curve in order to
determine tmax
k
, a limited enumeration can be
performed. The range of values for each parameter
of the opponent’s estimated concession curve to be
searched is bounded by opponent’s offer and other
parameters.
The heuristic for agent i is summarized below.
1. Get the weights w
k
for the utility function u
i
(x)
of the human principal.
2. Get value of Q
i
3. Set s=0, t
′ = 0 and q ′ = 0.
4. If((q
′ < Q
i
)∧ (t ′ <Tmax
i
) then select an
opponent with public information (Q
o
, x
o1
) such
that (Q
o
/(Q
i
-q ′ ))(u(x
o1
)) is the highest across all
non-busy opponents, set s = s+1, j=1; else stop.
5. Get values for the following: r
i
, tmax
is
, x
i1
6. If (x
i1
= x
o1
), agreement is reached, stop thread,
transact min(Q
o
, (Q
i
- q ′ )), set q ′ = q ′ + min(Q
o
,
(Q
i
- q ′ )), go to Step 4.
Repeat Steps 7- 16 for iteration j of thread s
7. Set j = j+ 1. Get offer x
oj
from the opponent.
8. If (x
ij
-1 = x
oj
), agreement is reached, stop
thread, transact min (Q
o
, (Q
i
- q ′ )),
set q
′ = q ′ + min(Q
o
, (Q
i
- q ′ )), go to Step 4.
9. If (j
≥ 4) then
for each k such that (x
ij
-1
k
≠ x
ojk
),
using x
o1
,..,x
oj
, estimate tmax
k
, β
k
, mn
k
,
mx
k
, by fitting a curve of the form given
by (1) and minimizing the sum of squared
errors. Use user-supplied bounds while
enumerating parameters to search for the
best curve and then use tmax
k
in (2) to
compute t
ijk
.
10. If (j <4) then for all k set t
ijk
= tmax
is
- j.
11. If (t
ijk
> 0) then compute τ
ijk
using (3), cr
ijk
using (4), s
ijk
using (5), and x
ijk
using (6).
12. For all k such that (x
ij
-1
k
= x
ojk
) set x
ijk
= x
ij
-1
k
.
13. If(x
ij
= x
ij
-1 ≠ x
oj
)
then for all k
∈ I
i
such that ( x
ijk
> y
lk
)
set x
ijk
= max(y
lk
, r
ik
, x
ojk
)
for k
∈ D
i
such that ( x
ijk
< y
lk
)
set x
ijk
= min(y
lk
, r
ik
, x
ojk
)
14. If(x
ij
= x
oj
), agreement is reached, stop thread,
transact min (Q
o
, (Q
i
- q ′ )), set q ′ = q ′ + min(Q
o
,
(Q
i
- q ′ )), go to Step 4.
15. If (((x
ij
= x
ij
-1) ∧ (x
oj
= x
oj
-1)) then
if (
∀ k( ( x
ojk
≥ r
ijk
) when k ∈ I
i
and ( x
ojk
≤
r
ijk
) when k ∈ D
i
then x
ij
= x
oj
and reach
an agreement,
else stop thread, no agreement reached,
go to Step 4.
16. If(((x
ij
= x
ij
-1 = r
i
) ∨ (j= tmax
is
)) ∧ ( (Q
i
- q ′ )/
Q
i
)/( (Tmax
i
- t ′ )/ Tmax
i
) > 1) then
if (
∀ k( ( x
ojk
≥ r
ijk
) when k ∈ I
i
and ( x
ojk
≤
r
ijk
) when k ∈ D
i
then x
ij
= x
oj
and reach
an agreement;
else stop thread, no agreement reached,
go to Step 4.
Else stop thread, no agreement reached, go to
Step 4.
In Step 1, the weights w
k
assigned to the
negotiation issues (i.e., price and period in the
current paper) are obtained from the human
principal and then incorporated in a commonly used
additive utility function of the form u(price, period)
= w
price
u
1
(price) + w
period
u
2
(period), where u
1
and
u
2
are normalized linear functions of price and
period respectively. The quantity to be transacted by
the agent in the market place is then specified to the
agent in Step 2. In Step 3, the time counter t
′ is
started. The value of t
′ is constantly updated by a
clock. The thread count, s as well as the quantity
transacted, q
′ are also initialized to zero in Step 3.
In Step 4, an available opponent is selected for
negotiations with the highest value for the metric
(Q
o
/(Q
i
-q ′ ))(u(x
o1
)) which is the product of the ratio
of opponent’s quantity and the quantity remaining to
be transacted, and the utility value of the starting bid
of the opponent. This metric enables the agents to
select an opponent in the pool, who has large
quantity to transact as well as an attractive starting
bid that gives high utility value to the agent. In Step
4, an opponent is only selected if some quantity still
remains to be transacted (i.e., q
′ < Q
i
) and the time
window has not expired (t
′ <Tmax
i
). In Step 5, the
agent obtains its human principal’s reservation
values along with the bound on the number of
iterations for negotiations for the current negotiation
thread as well as the starting bid from its human
principal. Step 6 is needed to check if an agreement
is reached in the very first iteration.
When iterations are four or higher, then offer
points available from the opponent are adequate to
run a curve fitting procedure in order to estimate the
number of iterations the opponent is targeting. In
Step 9, the curve-fitting procedure is run based on
the exponential curve in (1) to estimate tmax
k
. When
the iterations are less than four, the number of offer
points of the opponents is not adequate to compute
good estimates of tmax
k
. In this case, the total
number of iterations is estimated as tmax
is
, the initial
bound that is set by the human principal of the
DESIGN AND EVALUATION OF AGENT-BASED NEGOTIATION HEURISTIC FOR ONLINE NEGOTIATIONS
95

agent. The number of iterations remaining is tmax
is
– j, where j is the number of iterations that has
elapsed. As long as the number of iterations
remaining is one or more, settlement target,
concession rate, step size and the new bid is
computed in Step 11. For negotiation issues for
which agreements have been reached, the last bid
value is the current bid value as seen in Step 12.
If the current bid is the same as the last bid and
is not equal to the opponent’s bid (Step 13), then the
current bid value is set to the market value subject to
the bounds set by own reservation value and
opponent’s bid. If now an agreement is reached
(Step 14), then quantity can be transacted. If the
current bid is the same as the previous bid and the
opponent’s current bid is also the same as his/her
previous bid, then an agreement can be reached if
the reservation value constraints are satisfied (Step
15). Finally in Step 16, if the current bid is the same
as the previous bid and equals own reservation
values, or if the total number of iterations planned
tmax
is
, is exhausted, and there is a sense of urgency
as given by the metric: ((Q
i
- q ′ )/ Q
i
)/( (Tmax
i
- t ′ )/
Tmax
i
), when its value is greater than 1, then an
agreement with the opponent can be reached if the
own reservation value constraints are met.
Otherwise negotiations are terminated.
4 THE RESEARCH HYPOTHESIS
AND EMPIRICAL STUDY
Both human and agent buyers constantly learn from
and adapt to each other’s behaviors and/or engage in
strategic moves in response to opponent behavior.
We however conjecture that automated agents
implementing our heuristic are likely to have an
upper hand in this negotiation process, by virtue of
their ability to quickly and accurately estimate
uncertain negotiation parameter such as the number
of opponent moves. Estimation of such parameter
often places substantial cognitive demands on
humans. The performance gap between humans and
agents will tend to magnify with increasing
complexity of the negotiation process, such as the
number of negotiation issues. Hence we
hypothesize:
H1: Electronic agents will perform significantly
better than human negotiators when negotiations
involve multiple issues
To test the above hypothesis and the
performance of agents, we conducted a pilot
experiment to identify the differences between
performance and efficiencies achieved by humans
and electronic agents while trying to buy fixed
quantities of goods. The experiments involved
buyers and sellers negotiating over two issues: price
and the number of months of interest free payment
period. The dependent variable in the experiments
was negotiation performance, i.e., the utility gained
by the settlement over the utility of own reservation
values. The objective of each negotiator was to buy
or sell at values that maximize his/her utility.
To make the negotiation environment as
realistic as possible, we created experiments similar
to a commodities exchange (Chicago Board of
Trade 1998). Specifically, to model price discovery,
the price of the last trade was displayed to all buyers
along with the financing period. All sellers were
electronic and used a hybrid Boulware/Conceder
algorithm (different from the current heuristic) to
make offers. Seller agents used negotiation
parameters based on current market values. Human
subjects played the role of buyers.
To conduct the experiments, we sought subjects
with prior experience or coursework on
negotiations. Subjects received token cash
incentives based on their negotiation performance
based on their utility metric. We elicited weights for
utility functions from human subjects. The utility
functions used were the commonly used linear
additive function of the form presented in Section 3.
For the actual negotiation sessions, all subjects were
assigned identical reservation values (80 for price
and 3 months for period) and were required to buy
identical quantities (20 units) of the commodity.
Parameters δ
1
and δ
2
were set to 0.05. Experiments
were conducted under two market configurations. In
the first set of negotiations, market supply was half
the total demand. In the second set, supply was
twice the actual demand. To make the most efficient
use of subjects’ time, two rounds of negotiations
were conducted for each market configuration. Half
the subjects in each round used their surrogate
agents implementing the heuristic presented in this
paper, and the other half negotiated on their own. In
the second round, subjects that used agents in the
first round negotiated without agents, while subjects
that did not use agents, now used surrogate agents in
the second round to buy in the market place. We
had eight subjects for the experiments and the
supplies were appropriately calibrated for the two
market configurations.
The results for successful transactions during
the experiments are shown in tables 2 and 3.
Specifically, Table 3 contains results from t-tests for
differences. As can be seen from Table 3, fewer
transactions were made when supplies were limited.
ICEIS 2004 - SOFTWARE AGENTS AND INTERNET COMPUTING
96

Table 2: Summary Statistics
Demand/Supply= 2 Demand/Supply = 0.5
TYPE N Mean Std.
Deviation
N Mean Std. Deviation
Close price Agent 4 74.1700 3.28996 9 73.0667 4.35895
Human 9 75.7667 5.13323 7 72.7814 4.32834
Close period Agent 4 4.5425 .50704 9 4.4344 .89605
Human 9 3.7733 .61640 7 3.4571 .40766
Iterations Agent 4 7.50 3.697 9 4.44 1.236
Human 9 9.44 2.128 7 5.14 1.345
Table 3: t-test results
Demand/Supply =2 Demand/Supply = 0.5
Variable t Df Sig
(2-tailed)
mean
diff
T Df Sig
(2-tailed)
mean
diff
Close price -0.67 9 0.52 -1.60 0.13 13 0.9 0.29
Close period 2.36 7 0.05 0.77 2.91 11 0.01 0.98
Iterations -0.98 4 0.38 -1.94 -1.07 12 0.31 -0.7
The results indicate that there were no
significant differences between humans and agents
in prices. However, agents performed significantly
better than humans on negotiating the duration of
the financing period. The difference was significant
across market conditions, supporting Hypothesis 1
regarding the superiority of agents in multi-issue
negotiations. This result also suggests that agents
should be preferred when negotiations involve
multiple issues.
An obvious limitation of these results is the
small sample size of the pilot. In our experiments
following this pilot, we will address this limitation
by performing more experiments with human
subjects. Also, we will vary the number of issues to
ascertain the performance of agents with respect to
humans as the number of issues change. Some
subjects were uncomfortable with the monotonic
nature of the negotiations and suggested that they be
allowed to lower their offer prices in return for
conceding on period. We also plan to improve the
human interface based on subject feedback and
refine the heuristic further based on the
experimental results.
REFERENCES
Chari, K., & Seshadri, S. (2004). Next Generation B2B
Commerce Using Software Agents. Intelligent
Enterprises of the 21
st
Century, Idea Group
Publishing, Hershey, PA 17033.
Chari, K., & Bhattacherjee, A. (2002, December). Multi-
Thread Automated Negotiations Using Learning
Agents. Proceedings of the Workshop on Information
Technologies and Systems (WITS), Barcelona, Spain.
Chavez, A., & Maes, P. (1996, April). Kasbah: An agent
marketplace for buying and selling goods.
Proceedings of the First International Conference on
the Practical Application of Intelligent Agents and
Multi-Agent Technology, London.
Chicago Board of Trade (1998), Commodity Trading
Manual, Chicago, IL.
Faratin, P., Sierra, C., & Jennings, N. R.
(1998). Negotiation Decision Functions for
Autonomous Agents. Robotics and Autonomous
Systems, 24 (3-4): 159-182.
Kraus, S., & Wilkenfeld, J. (1993). A Strategic
Negotiation Model with Applications to an
International, Crisis. IEEE Transaction on Systems
Man and Cybernetics, 23(1), 313-323.
Oliver J.R. (1996, Winter). A Machine Learning Approach
to Automated Negotiation and Prospects for Electronic
Commerce, Journal of Management Information
Systems, 13, 3 126-164.
Sycara K., (1990). Negotiation Planning: An AI approach.
European Journal of Operational Research, 46, 216-
234.
Zeng D., & Sycara, K. (1998). Bayesian Learning in
Negotiation. International Journal of Human-
Computer Studies, 48, pp. 125-141.
Zeuthen, F. (1968). Problems of Monopoly and Economic
Warfare, Routledge and Kagan Paul, London.
DESIGN AND EVALUATION OF AGENT-BASED NEGOTIATION HEURISTIC FOR ONLINE NEGOTIATIONS
97