![](bg5.png)
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.
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