Decision Support Systems 46 (2009) 755–762
Contents lists available at ScienceDirect
Decision Support Systems
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d s s
Reservation price reporting mechanisms for online negotiations
Seungwoo Kwon a,1, Byungjoon Yoo b,⁎, Jinbae Kim a,2, Wei Shang c,3, Gunwoong Lee d,4
a
Korea University Business School, Anam-dong, Seongbuk-gu, Seoul 136-701, South Korea
Graduate School of Business, Seoul National University, 599 Gwanangro, Shinlim9-dong, Gwanakgu, Seoul 151-916, South Korea
c
Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Room429, SiYuan Building. No.55, East Zhongguancun Rd. Haidian Dist.,
Beijing, 100190, China
d
Krannert School of Management, Purdue University, West Lafayette, IN 47907-2056, USA
b
a r t i c l e
i n f o
Available online 20 November 2008
Keywords:
Online negotiation
Reservation price
a b s t r a c t
To facilitate online negotiations, this paper proposes a reservation price reporting mechanism (RPR) and its
extended version (ERPR), in which negotiators are invited to report their reservation price to a third-party
system before initiating negotiations. Analyses using analytical models show that sellers and buyers report
their true reservation prices under certain conditions with respect to the back-dragging costs. Analytical
models also show that total social welfare can be increased by two reservation price reporting mechanisms.
Then lab experiments are conducted to compare the performance of RPR, ERPR and the traditional direct
bargaining (TDB). Consistent with the analytical models, results of the lab experiments show that RPR and
ERPR reduce the number of negotiation rounds before reaching an agreement and increase negotiators' social
welfare. These lab results testify to the efficiency of RPR and ERPR over TDB.
© 2008 Elsevier B.V. All rights reserved.
1. Introduction
Modern information technologies facilitate convenient information exchange with less temporal and geographical restrictions and
provide decision support functions with higher expected profits.
Online negotiations may enable negotiators to achieve better payoffs
by facilitating information exchange, even though the information
provided is somewhat noisy [1]. Online negotiations can be conducted
directly between participants by means of information technology
such as emails or virtual meetings. However, one of the most
promising ways is third-party mediated online negotiation. A third
party may neutrally serve as a mediator or host of an e-marketplace.
Buyers and sellers get together at a third-party website to negotiate
with each other. Practitioners perceive that internet-based online
negotiation can be useful, but still have low confidence in pure online
negotiation especially when risks are involved [7].
Online negotiation can be classified according to the number of
parties involved in: bilateral negotiations and multilateral auctions
[10]. Mechanisms for e-auctions are widely discussed. Most e-auction
mechanisms are designed on the basis of existing auction mechan-
⁎ Corresponding author. Tel.: +82 2 880 2550.
E-mail addresses: winwin@korea.ac.kr (S. Kwon), byoo@snu.ac.kr (B. Yoo),
jinbae@korea.ac.kr (J. Kim), shangwei@amss.ac.cn (W. Shang), lee633@purdue.edu
(G. Lee).
1
Tel.: +82 2 3290 2604.
2
Tel.: +82 2 3290 1958.
3
Tel.: +86 62565817.
4
Tel.: +1 765 494 4375.
0167-9236/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.dss.2008.11.006
isms, such as English Auction or Vickery Auction. Trust and shillbidding are among the main issues to be resolved in terms of
mechanism design [14]. However, there is little research on mechanism design for bilateral electronic negotiations.
Another way to use information technology for negotiation is the
Negotiation Support System (NSS). NSS has been evolved from the
Decision Support System (DSS). NSS is a man-machine interaction
system that assists negotiators in analyzing and solving negotiation
problems by helping them structure their preferences and view data
regarding negotiations [15]. NSS, as a result, leads negotiators to make
better decisions and maximize profits (e.g., Negotiator [2], Negoisst
[12]). Existing NSSs mostly try to imitate the traditional face-to-face
(F2F) negotiations or decision support throughout the process of
online negotiation [5]. The suggested benefits of using NSS mainly
include helping negotiators construct their interests and offering
them some kind of post-transaction settlement [3] or the automation
of a negotiation process without human agents by using intelligent
agents [4]. Although issues such as preference elicitation and conflict
resolution have been studied extensively, very few studies employ
mechanisms beyond the frame of traditional F2F negotiation. Specially
designed negotiation mechanisms are indispensable for more effective online negotiations.
This paper focuses on designing a negotiation support mechanism
to support bilateral business negotiations between agents. Two new
mechanisms, reservation price reporting mechanism (RPR) and
extended reservation price reporting mechanism (ERPR), are proposed. We examine analytical models under the proposed mechanisms from an economic perspective. Then, we assess the proposed
mechanisms in the laboratory from a psychological perspective.
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S. Kwon et al. / Decision Support Systems 46 (2009) 755–762
2. Economic models for bilateral negotiation
Economic models on negotiations originated to explain people's
behavior and predict the outcome of game theory [13]. People's
behaviors in negotiations are usually modeled as players' strategies,
which are indicated by sequences of bidding prices. A negotiator's
payoffs are generally calculated by the differences of the deal price and
their costs or reservation prices. Expected outcome of a negotiation is
predicted by the equilibrium of a particular game. Sophisticated
economic models of bilateral negotiations have been developed. For
the circumstance that two parties bid in turn and both suffer a certain
amount each round, both parties' bidding strategies and final
solutions can be predicted by Rubinstein's model [11]. Based on this
model, there are further studies on one-sided incomplete information
settings [8] and two-sided information settings [6].
Most economic negotiation models consider only one issue of
price, since price can always be generalized as a utility function in a
multi-issue negotiation problem according to utility theory. This
simplification is necessary when we focus mainly on the bidding
strategy and final outcomes. Contextual factors which influence the
process of negotiation are usually studied in behavioral negotiation
studies [9] and are beyond our economic approach. Therefore,
without losing any generality, the price bargaining between a buyer
and seller is taken as the context of the bilateral negotiation model in
this study.
Since negotiators engage in negotiations for their own interest,
how much they can get from the negotiation is the most important
factor influencing their behavior. As a result, a negotiator's gain is
usually referred to as his payoff. For the simplest case of price
bargaining from an economic perspective, the seller's payoff can be
calculated by the final deal price minus his/her cost and the buyer's
payoff can be measured by his/her budget price minus the final deal
price.
To ensure minimum payoffs, the negotiator always has a baseline
or resistance point, which means he or she will not continue a deal if it
is under this baseline. For example, a seller has a minimum price to
accept in mind. This minimum price is the seller's baseline. The
buyer's baseline is the highest price he or she is willing to pay for the
object being negotiated. This baseline is referred to as the buyer's
willingness-to-pay (or seller's reservation price). When the buyer's
willingness-to-pay is lower than the seller's reservation price, then
there is almost no chance of a deal. This kind of situation is referred to
as a negative bargaining zone. In each round of negotiation, costs such
as time, money and labor are involved in the bidding. If a negotiator
rejects an offering but continues to drag the partner(s) into another
round of negotiations, bidding costs as well as opportunity loss will be
incurred by both sides. Bidding cost and opportunity loss are referred
to as back-dragging cost.
3. Mechanism design for online negotiations
3.1. Reservation price reporting mechanism
In the RPR mechanism, negotiators are asked to report their
reservation prices (from sellers) or willingness-to-pay (from buyers)
to a third-party before they start negotiations. Specifically, a buyer is
asked to report the highest price that she can accept and a seller is
asked to report the lowest price that she can accept. When a buyer's
willingness-to-pay is higher than a seller's reservation price (i.e., the
negotiation is in a negative bargaining zone), there is no possibility
that an agreement can be reached. Therefore, from a theoretical
perspective, revelation of the reservation price can allow negotiators
to avoid wasting time and energy in a negotiation with a negative
bargaining zone. In practice, however, revelation of the reservation
price and willingness-to-pay could be risky, since the other party will
attain more negotiation power by capturing private information.
In the RPR mechanism, negotiators report reservation price or
willingness-to-pay to the electronic third-party. The electronic thirdparty is regarded as more neutral and more reliable by negotiation
participants than the physical third-party. Therefore, negotiators can
avoid useless negotiations in the negative bargaining zone using the
RPR mechanism. It should be noted that ‘reservation price’ in this
study does not have the same meaning as ‘reservation price’ in an
auction where the reservation price is known to bidders. In reality, the
seller's reservation price or the buyer's willingness-to-pay is rarely
announced in negotiations. If the reservation price or willingness-topay is known to the opposite party, then the party who released the
information would be placed at a disadvantage in the negotiations.
The RPR mechanism is conducted in three steps: 1) Potential
sellers and buyers report their reservation prices or willingness-topay to the mediation system. 2) The system checks whether a positive
bargaining zone exists between pairs of buyers and sellers. If so, then a
negotiation session is initiated. Otherwise, the process terminates. 3)
If a negotiation session begins, the buyer and the seller bid in turn
until a proposal is accepted by both sides or one side quits. In our
study, we focused on price negotiations, which may be generalized to
multi-criteria cases when the utility of different issues can be
calculated in one dimension.
To illustrate how the RPR mechanism works, an example of trading
used cars is presented as follows. Suppose that used cars are traded on
a website and the website requires all participants to submit their
reservation prices or willingness-to-pay to the system. A used car
seller first advertises the car on the website. The seller submits a
reservation price, say $1200, and other product information to the
system. The reservation price of the seller is not revealed to potential
buyers. Potential buyers can visit the website and freely review the
product information. If a buyer is interested in the used car, he is
required to report his willingness-to-pay to the system. The buyer's
willingness-to-pay is not revealed to the seller. Suppose the buyer
submits a willingness-to pay of $1100. Then the buyer's willingnessto-pay is lower than the seller's reservation price of $1200, which
means there is no possibility of agreement. The system notifies this
fact to both participants and the negotiations do not start.
Now suppose that the buyer submits a willingness-to-pay of
$1500. Then the maximum price the buyer is willing to pay is higher
than the seller's reservation price, which means that there is a positive
bargaining possibility. The system lets the two parties start negotiations. The seller makes the first bid at $1550. The buyer cannot accept
this price, but is aware that the lowest possible selling price is lower
than his willingness-to-pay. Therefore, the buyer refuses the first
proposal and makes a counterbid of $1250. While this bid is within the
seller's acceptable price range, the seller wants a higher profit. Hoping
that the buyer will accept a higher price, the seller proposes $1350.
The buyer accepts the proposed price because the price is within the
acceptable range and does not want to continue bargaining. However,
even when the seller's reservation price is lower than the buyer's
willingness-to-pay, it is possible that a deal can not be made. For
example, after a number of rounds of bids, the buyer or seller may
decide that continuing the negotiation is not worthwhile and
terminate the negotiation without reaching a deal.
3.2. Extended RPR mechanism
Offering more information may lead to higher efficiency. For
example, Priceline.com, an online site, sometimes provides bidders
extra information, such as a message, “Your bid is too far from
acceptable.” With this message, the bidder has an option of increasing
the bid price. This extra piece of information makes the whole
negotiation process quicker without revealing too much private
information, such as reservation price or willingness-to-pay.
Bidders tend to bid far from the baseline, especially at the early
stages of negotiation, to ensure more room to negotiate. This strategy,
S. Kwon et al. / Decision Support Systems 46 (2009) 755–762
however, is not efficient because if there is a larger bargaining zone, it
will take more time for the negotiators to reach an agreement. Thus,
both sides will incur greater costs in terms of bidding and time.
Therefore, we designed a guiding mechanism during negotiations,
which is similar to the message in Priceline.com. Before a bid is
submitted, the user has a chance to alter it with the system's advice.
For example, if the bidder decides to bid $1000, he receives the
system's advice to bid higher, because $1000 is much lower than the
seller's reservation price. That is, the system informs the bidder that
the price $1000 is too low and a higher price may have a greater
chance to be accepted. Given this information, the bidder may
increase the bid to get a quicker deal or the bidder may not change
the bid if he is not eager to make a deal right away.
The guiding mechanism should be carefully designed, otherwise
the bidder may find out the seller's reservation price by analyzing the
pattern of the system's advice. Therefore, the following considerations
should be taken into account when editing the guiding mechanisms:
First, the advice must be given only once each time. Second, the
criteria should be designed based on some random coefficients. More
details on this will be presented in Section 5.
4. Analytical models
buyer's reaction. Herewith, the seller's expected utility of price PS (t) at
time t is:
EUS ðPS ðt Þ; tÞ = US ðPS ðtÞ; tÞ Prðbuyer acceptsÞ + EUS ðt + 1Þ
Prðbuyer bargainsÞ + U0S ðtÞ Prðbuyer quitsÞ
A1. Two agents, a buyer and a seller, are involved in price bargaining.
A positive bargaining zone exists, where the deal price must be
decided within the zone.
A2. Each agent tries to maximize his or her own utility. Payoffs can
be calculated by the difference between agreed price and
reservation price.
A3. The seller's own reservation price, the minimum price to sell, or
the buyer's willingness-to-pay, the maximum price to pay, is
exogenous and held privately, but since the probability
distribution of all agents' reservation prices and willingnessto-pay are uniformly distributed between Pmin and Pmax, the
knowledge about the distribution of reservation prices and
willingness-to-pay is considered as common knowledge.
A4. Agents bid in turn. Each agent's bidding price sequence is
monotonic.
A5. Time is precious. Failure to make a deal at a certain round will
cost both agents a fixed amount.
A6. Each agent is risk averse.
4.1.2. Payoff structure
Without losing generality, we examine the seller's payoff structure.
Suppose PS(t) is the price proposed by the seller at time t. Seller's
utility of PS(t) is represented by function US(PS(t), t), if buyer accepts
PS(t). However, the buyer has two more options, one of which is to quit.
If the buyer quits the negotiation, then the seller can only have U0S (t) for
leaving the negotiation at time t. The buyer's third option is to bargain.
Suppose that the buyer is not satisfied with the seller's proposed price,
yet he is confident of making a better deal at a later time. Then the
buyer will choose to bargain, which means PS(t) is rejected and a new
price PB(t + 1) is proposed. The process will accordingly continue to the
next round and it is the seller's turn to make the decision whether to
accept, quit or bargain. Seller's utility in the next round can be denoted
by EUS(t + 1).
Since the seller is not certain whether the other party will accept,
reject, or bargain in response to the proposed price PS(t), a subjective
probability may be adopted to model the seller's belief about the
ð1Þ
and Prðbuyer acceptsÞ + Prðbuyer bargainsÞ + Prðbuyer quitsÞ = 1
According to A2 and A5, an agent's utility of price P at time t can be
calculated by the difference between agreed price and reservation
price (RS) minus the back-dragging cost (CS per round) at time t.
Reservation price here is the minimum price at which the seller is
willing to sell the item under negotiation. Thus, the seller's utility
function is US(PS(t), t) = PS(t) − RS − (t − 1)·CS. Since quitting the negotiation does not bring either party any benefit, but results in both parties incurring costs, the payoff of ‘quit' option can be denoted as: U0S(t)=
−(t− 1)·CS and U0B(t)=−(t − 1)·CB.
For the expected utility of the next round, the best outcome is for
the parties to make a deal at PS(t) and the worst is for the buyer to quit
the negotiation. Therefore, we have −t·CS ≤ EUS (t + 1) ≤ PS(t) − RS − t·CS.
Let α be the coefficient of risk preferences, as follows:
EUS ðt + 1Þ = ð −t CS Þ ð1−α Þ + ðPS ðtÞ−RS −t CS Þ α = −t CS + ðPS ðtÞ−RS Þ
α; ð0 V α V 1Þ:
4.1. Basic model for the RPR mechanism
4.1.1. Assumptions
In order to assess the proposed RPR mechanism, we examine a
simplified basic model in this section. Some basic assumptions on the
negotiation process under the RPR mechanism are as follows:
757
For simplicity of analysis, we assume totally risk averse agents, and
α here is supposed to be 0, which refers to the seller's expected utility
gain from the worst case where the buyer quits the negotiation. With
this simplification, a closed form solution for optimal strategies can be
induced, and it is expected that all the results would hold even when α
is non-zero. The utility function is then as follows:
EUS ðPS ðt Þ; t Þ = US ðPS ðtÞ; tÞ Prðbuyer acceptsÞ + EUS ðt + 1Þ
Prðbuyer bargainsÞ + U0S ðtÞ Prðbuyer quitsÞ
= ðPS ðtÞ−RS − ðt−1Þ CS Þ Prðbuyer acceptsÞ−t CS
Prðbuyer bargainsÞ− ðt−1Þ CS Prðbuyer quitsÞ
ð2Þ
= − ðt −1ÞCS + ðPS ðtÞ−RS Þ Prðbuyer acceptsÞ−CS
Prðbuyer bargainsÞ:
4.1.3. Bidding strategy
In economic models, all subjects are supposed to maximize their
utility. That is:
½
Max EUS ðPS ðtÞ; tÞ = − ðt−1ÞCS + Max ðPS ðtÞ−RS Þ Prðbuyer acceptsÞ
PS ðtÞ
PS ðtÞ
−CS Prðbuyer bargainsÞ :
ð3Þ
The fundamental trade-off of our model is in accordance with the
general bargaining situation. If a higher PS(t) is proposed, the seller
may possibly obtain a higher profit; however, the possibility of buyer
acceptance would be lower.
Given the seller's proposed price PS(t), the buyer will choose an
action which makes him better off according to the payoff structure:
8
< UB ðPS ðtÞ; tÞ
EUB ðPB ðt + 1Þ; t + 1Þ
: 0
UB ðtÞ
; accept
; bargain :
; quit
ð4Þ
Based on the model proposed above, truth revelation and
efficiency of the RPR mechanism are examined in the following part
of this section.
4.2. Truth revelation in the RPR mechanism
Whether the reported reservation price is the same as the actual
one is crucial to the performance of the RPR mechanism. We therefore
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S. Kwon et al. / Decision Support Systems 46 (2009) 755–762
examine the agents' strategies and a possible equilibrium and then
analyze truth revelation in a risk-averse situation.
4.2.1. One-round bidding
In the context of one-round bidding, each side bids only once. If the
bidding price of one side is acceptable to the other side, a deal is made
at this price. Otherwise, the negotiation breaks down. Pmin is the
minimum price for the item in the market and Pmax is the maximum
price for the item in the market. As stated above in assumption A3,
suppose all the reservation prices of the seller (RS) and the
willingness-to-pay of the buyer (RB) are expected to be in the range
[Pmin, Pmax] and uniformly distributed, and all the traders, including
the seller and the buyer, know Pmax and Pmin. Suppose all the bidding
prices are in the range [Pmin, Pmax], then a negotiator will accept the
other party's offer. RPR informs negotiators about the existence of a
positive bargaining zone, which means that the willingness-to-pay of
the buyer (RB) is greater than the reservation price of the seller (RS).
In this case, if both negotiators are rational, the probability of quitting
the negotiation is theoretically zero because ‘quitting' is not a rational
strategy. When there is a positive bargaining zone, negotiators
can reach an agreement at the price that is less than the buyer's
willingness-to-pay and more than the seller's reservation price. In
this case, it is rational to reach an agreement since both the seller
and the buyer can benefit. According to Eq. (3), in order to
maximize his expected utility, the seller's bidding price PS should
satisfy:
PS
Pmax −PS
PS −RS
= ðPS −RS Þ −CS Pmax −RS
Pmax −RS
Pmax + RS −CS
:
2
RS + PS ðt−1Þ−CS
2
ð10Þ
PB ðtÞ =
RB + PB ðt−1Þ + CB
:
2
ð11Þ
If the first bidding price is known, then the recursive expression of
bidding strategy can be resolved as a dependent variable of the first
bidding price and time t:
1
1
t Pmax + ðRS −CS Þ 1− t
2
2
1
1
PB ⁎ðtÞ = t Pmin + ðRB + CB Þ 1− t :
2
2
PS ⁎ðtÞ =
ð12Þ
ð13Þ
According to the reservation-price-deal rule, a seller will accept
any offer that is higher than or equal to his or her reservation price and
a buyer will accept any offer that is lower than or equal to his or her
willingness-to-pay. According to the proposed mechanism, the final
deal price can be proposed by either the seller or buyer. Suppose there
are equal chances for each case:
+ PB ⁎ðtÞ PrðBuyer proposes the final dealing priceÞ
ð5Þ
then,
PS =
PS ðtÞ =
EP⁎ðt Þ = PS ⁎ðtÞ PrðSeller proposes the final dealing priceÞ
max EUS ðPS Þ = ðPS −RS Þ PrðRB z PS Þ−CS PrðRB bPS Þ
f B ðRB ÞdRB −CS ∫RPSS f B ðRB ÞdRB
= ðPS −RS Þ ∫PPmax
S
Therefore, if the proposed price of the seller is considered the
maximum possible deal price Pmax, and the minimum possible deal
price is Pmin of the buyer, then the situation is the same as that of a
one-shot bid within a single round. The pricing strategy of the seller
and buyer at time t (t N 1) can be induced from the previous section:
ð6Þ
The chance of a deal is the probability that seller's bidding price is
smaller than or equal to the buyer's willingness-to-pay, i.e.,
Pmax −PS
Prðdealing at first roundÞ = PrðRB z PS Þ =
Pmax −RS
RS + PS ⁎ðt−1Þ−CS 1 RB + PB ⁎ðt−1Þ + CB 1
+
:
=
2
2
2
2
ð14Þ
Suppose the extreme case where the bargaining zone is so small that
the maximum turns are needed before a price within the reservation
prices is proposed by one side. In this case, a deal is made when t → ∞,
and we can assume P ⁎ (t) ≈ P ⁎ (t − 1). If this is substituted into Eq. (14),
we have:
EP⁎ðtÞ =
RS + RB −CS + CB
:
2
ð15Þ
ð7Þ
If a seller proposes the final deal price with probability γ, and the
buyer proposes with probability 1 − γ, then the expected deal price is:
EP ⁎ (t) = (RS − CS)·γ + (RB + CB) (1 − γ).
If the back-dragging costs are the same for the two sides, the
expected deal price under the given mechanism is in accordance with
the “fair” allocation rule in common system-mediated mechanisms,
i.e., dividing the cake into two equal parts.
Similarly, the buyer's bidding price can be inferred. Then, the
chance to reach a deal is the probability of the buyer making a
counteroffer, as in Eq. (9).
4.2.3. Proof of truth revelation
According to Eq. (15), if the reservation price is truthfully reported,
then the seller's expected utility is:
Pmax + RS −CS
2
Pmax −RS
Pmax −
=
=
PB =
Pmax −RS + CS
:
2ðPmax −RS Þ
Pmin + RB + CB
:
2
ð8Þ
Prðnegative bargaining zoneÞ
RS + RB −CS + CB
Pmax −RS
RS −Pmin
−RS −CS :
=
2
Pmax −Pmin
Pmax −Pmin
Prðdealing at second roundÞ = ð1 −PrðRB z PS ÞÞ PrðRS V PB Þ
PB −Pmin
=
RB −Pmin
=
Pmin + RB + CB
−Pmin
2
RB −Pmin
EUTS = ðEP⁎ −RS Þ Prðpositive bargaining zoneÞ−CS
ð9Þ
RB −Pmin + CB
:
2ðRB −Pmin Þ
4.2.2. Equilibrium for risk-averse agents
Risk-averse agents perceive minimal expected utility on future
rounds under the condition that no deal is made in the current round.
ð16Þ
If the reservation price is falsely reported by increasing the
reservation price ΔRS N 0, then the seller's expected utility is:
EUFS =
ðRS + ΔRS Þ + RB −CS + CB
Pmax − ðRS + ΔRS Þ
−RS −CS
Pmax −Pmin
2
ðRS + ΔRS Þ−Pmin
:
Pmax −Pmin
ð17Þ
S. Kwon et al. / Decision Support Systems 46 (2009) 755–762
Comparing the expected utility:
EUTS −EUFS =
ΔR2S + ðRB + CB + CS −Pmax Þ ΔRS
:
2ðPmax −Pmin Þ
ð18Þ
Therefore, if the buyer's back-dragging cost is large enough to
satisfy CB + CS ≥ Pmax − RB (i.e., RB + CB + CS − Pmax ≥ 0), then there is no
need for the seller to report a false reservation price (as shown in
Fig. 1), since Eq. (18) will always be greater then zero, which means
truth-telling may bring more expected utility to the seller.
If CB + CS b Pmax − RB (as the dashed curve in Fig. 1.), then the seller
will increase his reservation price by ΔRS = Pmax − RB2− CB − CS for maximum
expected utility. When the seller makes the decision of whether to tell
the truth, he does not know the buyer's exact willingness-to-pay,
which is needed in order to evaluate whether truth telling is more
profitable. Since the possible price range of the product in the market
is common knowledge, however, the expected value of the buyer's
willingness-to-pay can be estimated by ERB = Pmax 2+ Pmin according to A3.
And the truth telling decision condition will be CB + CS z Pmax 2− Pmin . If
this condition is not met, then the seller will report a false reservation
price by ΔRS = Pmax − Pmin2 − CB − CS. The higher the sum of the back-dragging
cost, the less likely it is that a fake amount will be reported.
Similarly, we may infer that the buyer will also have an incentive to
tell the truth on this condition. If this condition does not hold, then the
likelihood of a false report will be ΔRB = Pmax − Pmin2 − CB − CS . Therefore, we
propose the following:
Proposition 1. If the sum of the buyer's and the seller's back-dragging cost
is no less than half of the difference between the maximum and minimum
prices, then both sides will report their true reservation price or willingness
ΔRS = 0
to-pay for the item. (
; when CB + CS z Pmax 2− Pmin ) In addition,
ΔRB = 0
both sides will be( more honest if the sum of the back-dragging cost is
0
0
0
ΔRS NΔRS
if CB + CS bCB + CS ).
relatively higher. (
0 ;
ΔRB NΔRS
4.3. Increased social welfare in the RPR mechanism
The RPR mechanism is superior to the traditional bargaining
mechanism because it may increase dealings by ensuring a positive
bargaining zone before the negotiation starts. Further, overall social
welfare is also expected to increase by decreasing total back-dragging
cost.
4.3.1. Decrease of the expected number of rounds
Deals may increase through the RPR mechanism by 1) terminating
the negotiation process before the first round, if there is a negative
759
bargaining zone; 2) facilitating trust among agents based on a positive
bargaining zone and truth-telling incentives. The free bargaining case
will be further examined and compared with the RPR mechanism in
the next section.
Aside from acceptance and rejection by rational agents, there
is a third possibility of termination (i.e., negotiation terminates
without further communication) in free bargaining without a deal
guarantee in RPR. Expected utility function in the context of free
bargaining is as shown in the following function. For one-round
bidding, we have:
max EUS ðPS Þ = ðPS −RS Þ PrðRB z PS Þ−CS PrðRS V RB bPS Þ + U0S PrðRB bRS Þ
PS
f B ðRB ÞdRB −CS ∫RPSS f B ðRB ÞdRB
= ðPS −RS Þ ∫PPmax
S
S
+ U0S ∫PRmin
f B ðRB ÞdRB
Pmax −PS
PS −RS
RS − Pmin
= ðPS −RS Þ − CS + U0S Pmax − Pmin
Pmax −Pmin
Pmax − Pmin
PS =
Pmax + RS −CS
:
2
ð19Þ
ð20Þ
As shown above, the pricing strategy is not different with the RPR
mechanism. However, the chance of a deal is different from that of the
RPR mechanism:
PrFREE ðdealing at first roundÞ = PrðRB z PS Þ =
=
Pmax −PS
Pmax −Pmin
Pmax −RS + CS
:
2ðPmax −Pmin Þ
ð21Þ
Suppose the possible range of deal prices [Pmin, Pmax] and the backdragging costs are the same in free bargaining and RPR; we may
compare this with Eq. (7):
PrFREE ðdealing at first roundÞ V PrRPR ðdealing at first roundÞ
PrFREE ðdealing at first roundÞNPrRPR ðdealing at first roundÞ
; Pmin V RS
; Pmin NRS
ð22Þ
This equation shows that when conflict is low (i.e., Pmin N RS), free
bargaining has a higher probability of reaching a deal in the first
round. On the other hand, when conflict is high (i.e., Pmin ≤ RS),
negotiations under RPR have a higher probability of reaching a deal in
the first round. Further, the probability of reaching a deal in later
rounds is higher under the RPR mechanism than free bargaining when
conflict is relatively high.
Therefore, compared to free bargaining as in the TDB mechanism,
the RPR mechanism facilitates a higher chance of obtaining a deal. At
the same time, the expected payoffs for agents under the RPR
mechanism are not lower than under free bargaining, since the pricing
strategy is almost the same in both cases. Therefore, we may conclude
that the RPR mechanism can function as an incentive for rational
agents.
As we have already proved above in Eqs. (21) and (22), the chance
of a deal in each round is increased using the RPR mechanism.
Therefore, under the RPR mechanism, the total expected number of
rounds will decrease accordingly. We propose the following:
Proposition 2. When seller's reservation price and buyer's willingnessto-pay are within the range of the minimum price and the maximum
price, negotiations under the RPR mechanism will have fewer rounds than
those under the TDB mechanism. (EtFREE ≥EtRPR, when RS, RB ∊[Pmin, Pmax]).
Fig. 1. Difference on expected utility.
4.3.2. Overall increase in return
According to our assumptions, in a certain round, bargaining under
the RPR mechanism can be considered as a zero-sum game, in which
one side's gain is the other side's lost. However, from the view of the
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S. Kwon et al. / Decision Support Systems 46 (2009) 755–762
whole negotiation process, if a deal is not made in a certain round,
both sides will incur some amount of back-dragging cost.
Usocial = US + UB = P⁎ −RS −CS Et⁎ Þ + ðRS −P⁎ −CB Et⁎ Þ = − ðCS + CB Þ Et⁎
ð23Þ
It has been proved that Et⁎ decreases under the RPR mechanism.
Therefore, we expect an average increase in terms of social welfare.
An overall increase in return is obtained under the RPR mechanism
as a result of: 1) eliminating occasions of a negative bargaining zone
which will lead to no deal; 2) setting up reservation-price deal rules
that help agents save time, since any bid that is between the
reservation price and willingness-to-pay is likely to end the negotiation without the need for further rounds.
4.4. The ERPR mechanism
Given the guidance such as ‘your bid is good' or ‘your bid is not
reasonable’, the agents may alter their bids before submission.
According to A4 and A5, after viewing the system's guidance, the
seller will lower his or her price or not change it and the buyer will
increase his or her bid or not change it. Suppose the seller will
alter his or her bid by ΔPS (ΔPS ≤ 0), then the seller's bidding price
will be PS + ΔPS. If the new bidding price is substituted in (7), then
PrERPR ðdealing at first roundÞ = Pmax 2−ðRPSmax+ C−SR−S Þ2ΔPS . Since ΔPS is no greater
than zero, the result is PrERPR (dealing at first round) ≥ PrRPR (dealing
at first round). Similar to previous discussion, the negotiations
under the ERPR mechanism were found to have fewer expected
rounds than those under the RPR mechanism since the chance of
acceptance is greater in each round under the ERPR mechanism.
Proposition 3. With extended bid information, the buyer and seller tend
to make greater concessions and rounds will be fewer in number under
the ERPR mechanism than under the RPR mechanism. (EtRPR ≥ EtERPR).
5. Experimental design
We conducted an experiment to test the effectiveness of the TDB,
RPR and ERPR mechanisms in a controlled negotiation context.
Combinations of buyer's willingness-to-pay and seller's reservation
price and back-dragging costs were designed to prove the three
propositions in our analytical model.
5.1. A prototype NSS
We developed a prototype NSS for the experiments. This system
should: 1) generate experimental negotiation sessions; 2) support the
TDB, RPR and ERPR mechanisms; 3) randomly assign buyers and sellers to
one negotiation session. Subjects who participated in the experiment
were asked to log into the NSS. Then, the system matched negotiation
pairs and informed the subjects about the reservation prices and
willingness-to-pay for the items up for negotiation. The system was
designed as a three-layered browser/server based architecture. Persistent
data entities, process handlers and interface presentations were
independent of each other so that modification of the system would be
easier. We implemented the system using a Java framework, which has
been used in several other applications and has been proved to be reliable.
5.2. Methodology
5.2.1. Participants and design
Sixty-seven undergraduate students, enrolled in introductory
courses in management sciences, participated in the experiment.
Participants received extra course credit in exchange for their
participation. In addition, participants received cash rewards based
on their performance in the experiment. The experiment design was a
2 × 3 factorial, with back-dragging costs (high vs. low) and types of
negotiation support system mechanism (TDB, RPR, ERPR).
5.2.2. Manipulations
5.2.2.1. NSS mechanism. There were 3 types of NSS mechanisms.
First, the TDB mechanism led negotiators to take turns bidding through
the website. Second, the RPR mechanism informed subjects of their
reservation price or willingness-to-pay. Then, subjects were asked to
report their true reservation price or willingness-to-pay to the system.
The subjects were warned that reporting a false reservation price or
willingness-to-pay might prevent the start of a negotiation session.
Third, the ERPR mechanism extended the RPR mechanism by
providing negotiators with advice on their bidding in addition to
reporting their reservation price or willingness-to-pay to the system. If
bids were too far from the reasonable range (25% range with respect to
the middle point of the seller's reservation price and the buyer's
willingness-to-pay), the system informed bidders that their bids were
not reasonable. Negotiators received the system's advice on their bids
before they were actually delivered to the negotiation partner.
Therefore, negotiators had one chance to alter their bids.
5.2.2.2. Back-dragging cost. There were 2 types of back-dragging cost
conditions. In the high back-dragging cost condition, each negotiator
(i.e., seller and buyer) lost 4% of the size of the bargaining zone when
an additional round was added. In the low back-dragging cost
condition, each negotiator lost 1% of the size of the bargaining zone
when an additional round was added.
5.2.3. Task and procedure
We adopted the scenario of trading laptop computers as presented in
the third section. Subjects were randomly assigned to one of the NSSs
(TDB, RPR, ERPR) and the role of buyer or seller by prototype NSS. The
system generated four negotiation sessions for each subject. The first
two sessions were practice sessions for subjects to get familiar with the
operation of the website. The next two sessions were real and the final
reward was calculated based on the results of these two sessions. One of
the real experiments was a high back-dragging cost condition (4% of the
size of the bargaining zone for seller and buyer each) and the other was
low back-dragging cost condition (1% of the size of the bargaining zone).
A negotiator did not know who his or her negotiating partner was. Only a
three digit user ID was revealed to the negotiating partner. Prior to the
bidding, the experimenters explained the process to the subjects. Based
on the profits made during the real sessions, participants were rewarded
with cash after the experiment.
6. Results and discussions
Table 1 summarizes the bidding records as well as the final results
of each negotiation session.
Table 1
Summary of results
TDB
RPR
ERPR
Total number of Sessions
Success rate (%)
38
0.97
53
0.91
32
0.88
Successful sessions
Number
Average number of rounds
Standard deviation
Average total profit
37
4.0
3.20
92.32
48
3.1
2.08
92.91
28
2.4
1.57
96.04
5
3.4
2.30
−5.00
4
1.3
1.26
−2.00
Failed sessions
Number
Average number of rounds
Standard deviation
Average total profit
1
5.0
−18.00
S. Kwon et al. / Decision Support Systems 46 (2009) 755–762
761
significance (p = .06). Therefore, Proposition 1 regarding truth revelation was supported.
Table 2
Truth revelation
Data
High back-dragging cost
Low back-dragging cost
Number of reports
Deviation ratio
Number of rounds
Statistical significance
70
6.9%
2.50
p b .10 (p = .06)
79
8.2%
3.18
Since the payoff structures were not the same, we normalized all
records to make them comparable to each other. Table 1 reports the
success rates, the average number of rounds to reach agreement, and
the average total profit the subjects achieved using each of the three
mechanisms. Negotiators had positive bargaining zones; therefore
reaching an agreement was possible. However, some negotiators
could not reach an agreement under all three mechanisms. In this
section, the results are discussed in terms of the number of rounds to
reach an agreement, truth revelation, and fairness.
6.1. Number of rounds and social welfare
Generally, the fewer the number of rounds to reach an agreement
and the higher the joint profits (i.e., the sum of two negotiators'
profits), the more efficient the negotiation sessions were. We
compared three mechanisms (TDB, RPR and ERPR) in terms of the
number of rounds in successful sessions, because fewer rounds
brought more social welfare as a result of lower back-dragging costs.5
Planned contrast was used to determine whether the RPR and ERPR
mechanisms shortened the number of rounds compared with the TDB
mechanism (proposition 2) [5]. Planned contrast indicated that the
RPR and ERPR mechanisms led negotiators to reach an agreement
faster than the TDB mechanism (t = 2.488, p b .01). Compared with TDB,
both RPR and ERPR are more effective in reducing the number of
rounds. Therefore, Proposition 2 of the analytical model is supported.
To test Proposition 3, we compared 2 NSSs (RPR vs. ERPR). The
result of the t-test shows that there was a significant difference
between the number of rounds of ERPR and RPR (t = 1.440, p b .10,
ERPR: 2.4 vs. RPR: 3.1). That is, participants reached an agreement
faster under the ERPR system rather than under the RPR system.
Therefore, Proposition 3 was supported.
6.2. Truth revelation
Proposition 1 of our analytical model was empirically tested; that
is, we tested whether negotiators were more honest when the sum of
back-dragging costs was relatively higher. In our experiment, the
extent of truth revelation was calculated by the average deviation ratio
(See Table 2 for results). We measured the deviation ratio by
calculating how much a negotiator's reporting price deviated from
the reservation price. The reservation price of the seller is the actual
cost of the item and that of the buyer is the true amount of money he
or she is willing to pay for the item. For example, the average deviation
ratio of a seller is lower when the reporting price is closer to the actual
cost of the item, while the average deviation ratio of a buyer is lower
when the reporting price is closer to the true amount of money he or
she is willing to pay. Therefore, the lower the average deviation ratio,
the higher is the level of truth revelation. We found that the average
deviation ratio of reporting price with high back-dragging cost (6.9%)
was lower than with low back-dragging cost (8.2%) with statistical
5
This negotiation exercise was a type of distributive negotiation due to there being
only one issue in the negotiation. However, this was not a zero-sum game because of
back-dragging costs. That is, the total profits of the two negotiators were affected by
back-dragging costs. In addition, the total profits were strongly correlated with the
number of rounds needed to reach an agreement in that both of them were associated
with back-dragging costs. Therefore, the significance test was performed only for the
number of rounds.
6.3. Fairness
In our experiment, sellers placed bids before buyers. That is, sellers
initiated the negotiation. In the TDB and RPR conditions, there were no
differences in terms of payoffs between initiators (i.e., sellers) and
followers (i.e., buyers). In the ERPR mechanism condition, however,
buyers' payoffs were much higher than sellers' (buyer: 61.9, seller:
34.2, t = 5.08, p b .001).
This result was interesting since it was not expected in our
analytical model. With the examination of subjects' bidding behaviors,
we found that the information provided in the ERPR sessions resulted
in less aggressive starting bids by the sellers. The sellers in the TDB and
RPR conditions made extreme first offers and used those as anchors. In
contrast, the sellers in the ERPR condition did not make extreme first
offers. Their offers were closer to their reservation price or willingness-to-pay than those of TDB and RPR. As a result, the sellers in
ERPR sold the object at cheaper prices. Future study should investigate
how to reduce the unfairness resulting from the information provided
in the ERPR mechanism.
7. Conclusion
Two new mechanisms (RPR and ERPR) were proposed to support
online negotiations by asking negotiators to report their reservation
price or willingness-to-pay to the NSS. In the RPR mechanism,
negotiators should report their reservation price or willingness-topay to the NSS at the start of a negotiation. Negotiations would be
initiated only when a positive bargaining zone was detected by the
NSS. The ERPR mechanism provided negotiators with information on
how far their bids were from the acceptable range before delivering
this bid information to the negotiation partners.
An analytical model was developed to find the equilibrium points and
assess the performance of the mechanisms. Under the assumption of
uniformly distributed reservation prices or willingness-to-pay and risk
aversion, the agents were shown to have incentives to reveal their actual
reservation price or willingness-to-pay to the NSS. When the agents did
not reveal the truth, higher back-dragging costs (resulting from more
rounds) led to smaller profits. The RPR mechanism was found to be more
efficient than the traditional free bargaining system in that negotiators in
RPR achieved higher social welfare than those in TDB. By the same token,
the ERPR mechanism was more efficient than the RPR mechanism.
In our lab experiment, the average social welfare level generated by
the three mechanisms was ordered as expected in our analytical model.
In addition, negotiators were more honest in the high back-dragging
cost conditions rather than in the low back-dragging cost conditions. We
found an interesting phenomenon in terms of fairness, which was not
considered in our analytical model. That is, the ERPR mechanism was
less favorable to the initiators of the negotiation compared with the
followers. The advice provided by the ERPR system discouraged the
initiator from opening the negotiation with an extreme offer. As a result,
the agreed price was favorable to the follower. In sum, the ERPR
mechanism resulted in an issue of fairness between the initiator and the
follower, even though higher levels of social welfare were engendered
compared with the RPR mechanism.
We conclude that the RPR mechanism helped negotiators achieve
better performance levels compared with the traditional TDB mechanism. Therefore, the RPR or ERPR negotiation support system is
recommended when designing an online negotiation mechanism. The
introduction of the RPR and ERPR mechanisms would be revolutionary
for the existing e-business trading mechanisms. The RPR and ERPR
mechanisms could be used successfully for electronic negotiations
where trusted third parties (e.g., e-marketplaces and intermediaries)
exist. Established e-commerce sites or e-marketplaces may introduce
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S. Kwon et al. / Decision Support Systems 46 (2009) 755–762
the RPR/ERPR mechanisms as an option for their customers who are
willing to report their reservation price or willingness-to-pay in order to
find a more reasonable bargaining partner.
However, for wider application of this study, assumptions of the
analytical model need to be eased in order to represent more general
cases, such as arbitrary reservation price distribution cases and risk
neutral or risk seeking cases. In a future study, we plan to consider the
various levels of agent risk preferences and further factors. Also, further
experiments on fairness and truth revelation with different conditions
are expected to reveal more detailed suggestions on NSS design.
Acknowledgements
The authors would like to thank the reviewers and editors for their
helpful comments and suggestions. Byungjoon Yoo thanks Management Research Center at Seoul National University College of Business
Administration for grant funding. Jinbae Kim and Seungwoo Kwon
appreciate the financial support of a Korea University Grant. This
research was partially supported by the Natural Science Foundation of
China (NSFC Project Number: 70471027, 70801059), and the China
Postdoctoral Science Foundation for Wei Shang.
Appendix A
Summary of notations
Notations Description
PS
PB
RS
RB
ΔRS
ΔRB
CS
CB
Pmax
Pmin
ERS
ERB
α
EP
EUtS
EUtB
The bidding price of seller in t (Endogenous variable)
The bidding price of buyer in t (Endogenous variable)
The reservation price of seller (Exogenous variable)
The buyer's willingness-to-pay (Exogenous variable)
The false report amount (Endogenous variable)
If ΔRS = 0, it means a seller truthfully reports the reservation price
The false report amount (Endogenous variable)
If ΔRB = 0, it means a buyer truthfully reports the willingness-to-pay for item
The back-dragging cost of seller (Exogenous variable)
The back-dragging cost of buyer (Exogenous variable)
The maximum price for the item in the market (Exogenous variable)
The minimum price for item in the market. (Exogenous variable)
The expected value of seller's reservation price
The expected value of buyer's reservation price
The coefficient of risk preferences
The expected final deal price
The seller's expected utility in t
The buyer's expected utility in t
[13] J. Von Neumann, O. Morgenstern, Theory of Games and Economic Behavior,
Princeton University Press, 1953.
[14] W. Wang, H. Zoltán, A.B. Whinston, Shill bidding in multi-round online auctions—
system sciences, Proceedings of the 35th Hawaii International Conference on
System Sciences, 2002.
[15] D. Wei, Electronic Business-Oriented Negotiation Support System (PhD dissertation, Harbin Institute of Technology, 2001).
Kwon, Seungwoo is an associate professor of management
at Korea University Business School. He received his Ph.D.
in Organizational Behavior and Theory from Carnegie
Mellon University. His articles have been published in
journals such as Journal of Personality and Social Psychology, Journal of Applied Psychology and Human Resource
Management. He received outstanding article award from
the International Association for Conflict Management
(2002) and was nominated for the best paper based on
dissertation (Conflict Management Division) at the Academy of Management conference (2002). His current
research interests include conflict management, negotiation, compensation, and justice in organizations.
Yoo, Byungjoon is working for Graduate School of Business
at Seoul National University as an assistant professor. Before
he joined Seoul National University, he worked at Korea
University and Hong Kong University of Science and
Technology. He received a Ph.D. in Information Systems
from Carnegie Mellon University. His research interests are
on B2B e-commerce, online auctions and pricing strategies
of digital goods such as software products and online games.
He has published on these topics in journals such as
Management Science, Journal of Management Information
Systems, and Journal of Organizational Computing and
Electronic Commerce. He has consulting experiences with
Korea Stock Exchange, Korea Game Industry Agency and other companies.
Kim, Jinbae is a professor at Korea University Business School.
Before he joined Korea University, he had been an assistant
professor at Boston University. He received an MBA from the
University of Chicago and a Ph.D. from Carnegie Mellon
University. His research interests are on empirical tests of the
agency model, performance-reward relation and corporate
governance. He has published various papers in journals
including Accounting Research Journal, Journal of Accounting
and Auditing Research, Asia-Pacific Journal of Accounting and
Economics and Asia-Pacific Management Accounting Journal.
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Shang, Wei is now a postdoctoral researcher at Institute of
Systems Science, Academy of Mathematics and Systems
Science, Chinese Academy of Sciences. She got her Ph.D. Degree
from Harbin Institute of Technology and visited Korea University for a year as a visiting student. Her research interests
include Negotiation Support Systems, Group Decision Making,
Macroeconomics Analysis Systems, and Software Engineering.
She has published papers in major conferences and journals
and participated in several national supported research projects
related to Negotiations and Group Decision-Making Systems.
Lee, Gunwoong is a Ph.D. student at Krannert School of
Management at Purdue University. Before his Ph.D. program,
he worked at Korea Association of Game Industry as a
research fellow. His research focuses on online reputation
systems and information economics. He has a MSc in
Management Information Systems, and a BSc in Computer
Science from Korea University.