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A reverse auction is a common way of executing supply chain sourcing. This article presents a spreadsheet-based game, the BucknellAuto game, that simulates the bidding process in a reverse auction. Students play the seller role and vie for the buyer's demand request by bidding against the automated competitors. The BucknellAuto game allows students to experientially learn not only the competitive bidding process of the reverse auction but also the implications of the auction parameters on the bidding competitiveness. The BucknellAuto game serves as a pedagogical tool for efficiently and effectively introducing the reverse auction to undergraduate students in a fun and interactive way.
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Game—Introduction to Reverse Auctions: The
BucknellAuto Game
Chun-Miin (Jimmy) Chen, Matthew D. Bailey
To cite this article:
Chun-Miin (Jimmy) Chen, Matthew D. Bailey (2018) Game—Introduction to Reverse Auctions: The BucknellAuto Game.
INFORMS Transactions on Education 18(2):116-126. https://doi.org/10.1287/ited.2017.0180
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Game
Introduction to Reverse Auctions: The BucknellAuto Game
Chun-Miin (Jimmy) Chen,aMatthew D. Baileya
aCollege of Management, Bucknell University, Lewisburg, Pennsylvania 17837
Contact:
jimmy.chen@bucknell.edu (C-MC); matt.bailey@bucknell.edu (MDB)
Received: August 15, 2016
Revised: December 8, 2016; March 13, 2017;
April 25, 2017
Accepted: April 28, 2017
Published Online in Articles in Advance:
October 11, 2017
https://doi.org/10.1287/ited.2017.0180
Copyright: ©2017 The Author(s)
Abstract. A reverse auction is a common way of executing supply chain sourcing. This
article presents a spreadsheet-based game, the BucknellAuto game, that simulates the
bidding process in a reverse auction. Students play the seller role and vie for the buyer’s
demand request by bidding against the automated competitors. The BucknellAuto game
allows students to experientially learn not only the competitive bidding process of the
reverse auction but also the implications of the auction parameters on the bidding compet-
itiveness. The BucknellAuto game serves as a pedagogical tool for efficiently and effectively
introducing the reverse auction to undergraduate students in a fun and interactive way.
Open Access Statement:
This work is licensed under a Creative Commons Attribution 4.0 Interna-
tional License. You are free to copy, distribute, transmit and adapt this work, but you must
attribute this work as “INFORMS Transactions on Education. Copyright ©2017 The Author(s).
https://doi.org/10.1287/ited.2017.0180, used under a Creative Commons Attribution License:
https://creativecommons.org/licenses/by/4.0/.”
Supplemental Material:
The game is available at https://doi.org/10.1287/ited.2017.0180.
Keywords:
reverse auction
spreadsheet simulation
experiential learning
supply chain sourcing
1. Introduction
In the context of supply chain management, compa-
nies aiming to reduce the procurement costs often exe-
cute a strategic procuring approach such as the reverse
auction (RA) (Schoenherr 2008, Hawkins et al. 2010).
The RA is typically executed electronically, offering a
variety of benefits to the supply chain as a whole and
has become the standard industry practice (Carter and
Stevens 2007, Sanders 2011). Introducing the concept of
RAs to students lacking industry experience is a chal-
lenge due to the scarcity of relevant pedagogical mate-
rials for teaching RA and its operations (Teich et al.
2005). To prepare business and industrial engineering
students for the issues that arise in implementing and
participating in RAs in practice, we present a pedagog-
ical simulation game with the primary learning goal
of allowing students to experientially learn the unique
RA bidding process through real-time thoughtful deci-
sions in fictitious scenarios using as little as seven min-
utes of class time. While much smaller in scale and
scope, the game is intended to play a similar role in
introducing RAs as classroom games such as the Beer
Game has done for issues in supply chain operations
(Kaminsky and Simchi-Levi 1998).
Structurally, the RA is a sourcing process in which
multiple sellers vie for the demand request from a sin-
gle buyer (Chen-Ritzo et al. 2005, Engelbrecht-Wiggans
and Katok 2006, Wan et al. 2012). Moreover, the bid-
ding price of the auction item is driven downward until
the sourcing period ends or no more sellers are will-
ing to bid any lower (Monczka et al. 2011). Figure 1
illustrates the difference between RAs and forward
auctions.
Researchers and practitioners have mixed opinions
about the RA (Sanders 2011, Monczka et al. 2011,
Hawkins et al. 2014). On the one hand, the RA may save
buyers substantial procurement-related costs or time;
on the other hand, the RA is primarily price-oriented
and may hurt sellers’ profitability as well as degrade
the seller-buyer relationship (Talluri and Ragatz 2004,
Giampietro and Emiliani 2007, Kumar and Chang 2007,
Pearcy et al. 2007). The debates have much to do with
the perceived appropriateness of using RA for the
given procurement project (Kumar and Maher 2008).
For example, the number of sellers, the administrative
costs for participating the RA, the competitors’ risk atti-
tudes, and whether the buyer would split the demand
quantity among multiple sellers are prominent factors
that can affect the competitiveness of the RA bidding
process (Engelbrecht-Wiggans et al. 2007, Anton and
Yao 1989, Klotz and Chatterjee 1995, Hawkins et al.
2010, Yeniyurt et al. 2011).
In recent years, using spreadsheet applications in
teaching management knowledge or decision-making
skills for undergraduate business students has become
common (Bell 2000, Teich et al. 2005, Jaureguiberry and
Tappata 2015). In this teaching note, we create a sim-
ple simulation game that can effectively highlight the
essence and issues of the RA for students (Lojo 2016).
Classroom games such as the famous Beer Game
have been recognized as a simple yet effective way of
illustrating complex ideas not easily taught through
116
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Chen and Bailey: The BucknellAuto Game
INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s) 117
Figure 1. Illustrations of the Forward and the Reverse Auctions
Seller 1
(supply of object Y)
)
Seller 2
(supply of object Y)
Seller 4
(supply of object Y)
Seller 5
(supply of object Y)
Seller 3
(supply of object Y)
Buyer 5
(demand of object X)
Buyer 4
(demand of object X)
Buyer 2
(demand of object X)
Buyer 3
(demand of object X)
Buyer 1
(demand of object X)
Forward auction
(e.g., Sotheby’s) Reverse auction
Single buyer
(demand of object Y)
Single seller
(supply of object X)
Bidding drives up
the object X price
Bidding drives down
the object Y price
d
B
i
d
B
i
d
B
B
i
i
d
B
i
d
B
i
d
B
i
d
B
i
d
B
i
d
d
B
i
traditional lectures (Griffin 2007). Similarly, computer
simulation games such as the Littlefield Technologies
are also widely used for teaching a variety of opera-
tions management concepts (Miyaoka 2005, Lojo 2016).
Given that most students are comfortable with these
types of activities, the RA simulation game presented
here is of high pedagogical value.
To this end, we present an RA spreadsheet-based
bidding game, called the BucknellAuto game. To our
knowledge, this is the first such spreadsheet-based
simulation teaching tool to introduce the concept of the
RA to students. In the BucknellAuto game, students
vie for the buyer’s demand quantity on 20 automotive
part items in the auctions by bidding against auto-
mated competitors. The individual student’s objective
depends on the instructor’s goal with the course since
the game can easily and meaningfully accommodate
single or multiple objectives. For example, the instruc-
tor can evaluate a student’s performance by at least two
measures: the number/percentage of bids won and the
total/average profit. That is, the students can focus on
winning as many auction bids as possible, being as
profitable as possible or both at the same time, while
being aware that the two objectives require different
strategies. The instructors may take advantage of this
game and discuss the trade-off between these two mea-
sures in the eventual performance evaluation. Regard-
less of which objectives are implemented for the game,
the instructor should fully clarify the student’s objec-
tive before the game is played . Our recommendation
is to take both measures into consideration by asking
the students to maximize the average profit and win
at least a certain number of auctions, which may be
the case the students will face in practice. That way,
the game becomes more challenging to the students
than the game with a single objective. Considering the
increased future use of RA , we aim to design a game
that motivates students’ learning of RA in a contextu-
alized setting (Tassabehji et al. 2006, Atkinson 2008).
With respect to auction structure, the BucknellAuto
game can be played as a first-price auction or as a
second-price auction. The first-price auction is a very
common and simple auction type yet a stepping stone
for learning other relatively more complex auction
types (Engelbrecht-Wiggans and Katok 2007). We sug-
gest playing the first-price auctions in the beginning
for two reasons. First, the auction winner in a first-price
auction is bound to supply the items at the price actu-
ally bid by the winner. As such, the first-price setting is
easily understandable to the auction participants due
to a straightforward awarding process. Second, sellers
in a first-price auction tend to place a bid greater than
their true costs to assure a positive profit if their bid
is selected. However, the optimal amount of markup
is not obvious, thus increasing the risk and compet-
itive nature of the game. We think struggling over
how much to bid above the true cost adds a realistic
dilemma that makes the game more appealing.
To increase the pedagogical value and flexibility of
the game, we allow the users to easily enable/disable
the second-price auction setting using a simple check
box in the game interface. In the conventional second-
price forward auction, the winner, or the highest bid-
der, honors the second highest bidding price. By the
same token, in the second-price reverse auction, the
lowest bidder honors the second lowest bidding price,
and the second lowest bidder honors the third low-
est bidding price. In terms of game play, the second-
price auction may lack some of the drama of the
first-price auction because risk-neutral sellers in a
second-price auction would likely always choose to bid
at their true costs due to the actual price being deter-
mined by the next highest bid (Milgrom and Weber
1982, Milgrom 1989, Kagel and Levin 1993). That is,
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Chen and Bailey: The BucknellAuto Game
118 INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s)
for those who are familiar with the auction theory, the
dominant bidding strategy in the second-price auction
can be obvious. This could also provide an opportu-
nity to instructors to allow students to constructively
discover this dominant strategy in the course of the
game.
The target users of the BucknellAuto game are under-
graduate business majors. Apart from basic spread-
sheet application proficiency, no specific skill sets or
knowledge are needed to play. The game can be played
by individual students independently or by pairs of stu-
dents sharing the same computer screen. Also, the game
can be used as a standalone session or accompany reg-
ular RA lectures. To date, 109 students from the Quan-
titative Reasoning or the Global Supply Chain Man-
agement course at Bucknell University have played the
game. In addition to positive qualitative student feed-
back , the statistical tests on the survey results strongly
support that the game will improve student’s under-
standing of RAs.
The remainder of the paper is organized as follows.
In Section 2, we explain the spreadsheet-based RA sim-
ulation BucknellAuto game. In Section 3, we report the
evaluation on the game effectiveness. In Section 4, we
conclude the paper with a summary.
2. Bidding Game
Students playing the BucknellAuto game are expected
to experience and struggle with the trade-offs between
profit margin in a submitted bid and the probability
of winning the auction. That is, the sellers’ trade-off is
that submitting a lower bid entails a greater probabil-
ity of winning but a lower profit if winning, whereas
submitting a higher bid entails a greater profit poten-
tial but lower probability of gaining the profit (Ding
et al. 2005).
In this section, we first introduce the auction vari-
ables and discuss their implications for bidding com-
petitiveness. Second, we introduce the pre-game setup
screens the students see before the game begins. Third,
we explain the main interface of the game. Fourth, we
provide a guide and recommendations for successfully
conducting the game in a classroom setting. Finally, we
address the game limitations.
2.1. Auction Variables
Inspired by Klotz and Chatterjee (1995), we incorpo-
rate the following key auction variables known to have
a significant effect on the competitiveness of the RA
bidding process in the BucknellAuto game.
2.1.1. Number of Invited Sellers (N). The number of
potential competitors Nin the RA positively corre-
lates to the RA bidding competitiveness. Intuitively,
the more participating sellers, the greater pressure the
sellers would feel when competing for the buyer’s de-
mand. That is, students’ average bidding prices tend to
drop as Nincreases. For simplicity, Nin the Bucknell-
Auto game is set to three or five, including the student
player(s).
2.1.2. Competitor Risk Attitude (β). The more risk-
averse the other sellers are, the less attractive entering
the auction is to the competitors. In the BucknellAuto
game, βdenotes how the profit gain is perceived by
the automated competitors. More specifically, β < 1,
β1, and β > 1represent risk-averse, risk-neutral, and
risk-seeking sellers, respectively. For example, the same
amount of profit gain would give the seller with β0.6
a smaller utility than it does to the seller with β1.0.
Klotz and Chatterjee (1995) indicate that the more risk-
averse the sellers are, the lower the price they will bid
(but no less than the true cost) due to the worry of not
winning.
2.1.3. Manufacturing Cost (Ci). The subscript iis the
seller index, where iN. We assume the manufactur-
ing cost per unit for every auction item is less than or
equal to $1. Rather than bidding on one unit of every
auction item, we arbitrarily scale the buyer’s demand
quantity for each auction item to 100 units to make
the auction more realistic. As a result, the total manu-
facturing cost per auction (Ci) is less than or equal to
$100. To impart idiosyncratic seller expertise on man-
ufacturing different auction items to the BucknellAuto
game, we randomize every seller’s total manufactur-
ing cost on the same auction item so that Ciuniformly
distributes between $0 and $100.
2.1.4. Bidding Price (bi). With the price of bi, the seller i
is willing to supply the 100 units of the auction item.
Thus, biis essentially the seller i’s revenue for a given
auction. Note that the BucknellAuto game is signifi-
cantly simplified such that for each auction, biis the
only input variable the studentsneed to contemplate: If
b>0, the student enters the auction; if b0, the student
does not enter the auction. In the meantime, the auto-
mated artifical intelligence (AI) sellers use some bid-
ding prices according to Klotz and Chatterjee (1995).
See Appendix Afor details. Consider the practical con-
cept of the buyer’s reserve price, i.e., the price at which
the buyer is willing to buy from some other source in
the marketplace (Emiliani and Stec 2002). We restrict bi
to be no greater than $100.
2.1.5. Dual Sourcing (α). In an RA, the buyer can
decide whether to split the demand quantity to be
awarded to the two lowest sellers. Under a dual-sourc-
ing scenario, the buyer awards a primary demand por-
tion α50% to the seller with the lowest price, and the
remainder, or 1α, to the seller with the second low-
est price. If α100%, then the buyer does not split the
demand quantity. Prior research shows that the buyer’s
decision on splitting the demand quantity, or so-called
dual sourcing, can affect every seller’s bidding behav-
iors. Intuitively, dual sourcing encourages the sellers’
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Chen and Bailey: The BucknellAuto Game
INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s) 119
participation as it reduces the chance that the partic-
ipating sellers end up winning nothing. Furthermore,
in the second-price (dual-sourcing) game Ciand biare
always based on the batch size of 100 units but will
be automatically adjusted (scaled) when the profit is
populated. See Appendix Bfor more details. Note that
under the dual-sourcing setting, the bidder that gets
the primary award (α) receives the second lowest price,
and the bidder that gets the secondary award (1α)
receives the third lowest price. If only one (two) bid-
der(s) participated in the auction, the buyer pays the
reserve price ($100) to the first (second) bidder.
2.1.6. Administrative Cost (K). In practice, providing
a seller’s quote according to the buyer’s specifications
takes time and effort and depends on the bid require-
ments (presentations, prototypes, etc.). In the Bucknell-
Auto game, we account for this and other overhead
cost factors with the administrative cost per auction, K.
Not entering the auction is the only way to avoid the
administrative cost. Intuitively, a high administrative
cost may discourage a seller from participating in the
RA as it reduces the auction profit margin. Thus, Kcan
be negatively correlated with the propensity of the sell-
ers’ participation in the RA. For simplicity, Kis invari-
ant with αand stays constant across all participants as
Figure 2. Game Background
well as all the auction items. Note that we do not disal-
low the total costs (K+Ci) to exceed the upper-bound
of bidding price ($100); in this case we hope students
would make a sensible decision and not enter such an
auction.
2.1.7. Seed (s). The seed is to control the random
number generator in Excel. We allow users to synchro-
nize the seed value to enable fair comparison of the
performance between the students, especially those in
the same groups/class.
2.2. Pre-Game Setups
This game was developed using Excel 2013 for the
Windows OS. The game was also tested using Excel
2016. The key operational procedure, regardless of
which Excel version is used, is the Excel Solver Add-in,
which must be enabled before running the simulation.
If enabled, “Solver” would appear under the Data tab
in the Ribbon; if not, then click “File” >“Options” >
Add-Ins” >Manage: Excel Add-ins and “Go” >check
the Solver Add-in box and “OK.
2.2.1. Game Background. Figure 2shows the informa-
tion screen that contextualizes the BucknellAuto game
for the students.
2.2.2. Auction Parameters. Figure 3allows the stu-
dents to conveniently choose some scenarios using the
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Chen and Bailey: The BucknellAuto Game
120 INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s)
Figure 3. Auction Parameters Using Drop-Down Boxes with
Default Values
drop-down boxes on the pre-determined values of the
BucknellAuto game parameters. Figure 4alternatively
allows the student to design any desired scenarios by
entering the parameter values after clicking the [Fine-
tune] button in Figure 3.
2.2.3. Game Tutorial. Figure 5shows the Bucknell-
Auto game instruction, the last screen before the game
begins.
2.2.4. Game Interface. Figure 6shows the main game
interface. To prevent user errors, we protect the cells
of the worksheet except cell C11 where the individual
student enters a bidding price between 0 and $100. For
further customization or edits, instructors can remove
the protection from the spreadsheet by clicking the
“Unprotected sheet” under the Review tab. A copy
of the BucknellAuto game can be obtained from the
authors or from the Institute of Transportation Engi-
neers (ITE) website.
Second-price option (Area A2:B2). The users can
play the game in the second-price auctions by checking
the box in A2 which would cause B2 to show “TRUE.”
To switch back to the first-price auctions, the users un-
check the box so B2 shows “FALSE.” The users can do
this change at any time, but it is recommended to stick
with one setting for a round of 20 auctions.
Game parameters (Area A3:B8). The users can
change the values of the BucknellAuto game variables
at any time by clicking the [Reset AI Sellers] button.
Figure 4. Auction Parameters Using Text Boxes with Default
Values
Game steps (Area C6:C13). In each auction, the stu-
dent must complete the following steps: (i) Click [Pre-
pare auction] button to clear any data generated from
the previous auction. (ii) Click [Mfg. cost] button to
randomly draw a manufacturing cost for producing
100 units of the auction item. (iii) In cell C11, enter 0
to not participate in the auction or a value less than
or equal to $100 to place a bid. (iv) Click [Auction
results] button to reveal the auction results. Note that
Figure 5. Game Tutorial
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Chen and Bailey: The BucknellAuto Game
INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s) 121
Figure 6. Screen-Shot of the Reverse Auction Bidding Game
this instruction is available by clicking the [Tutorial]
button.
Current results (Area E10:I18). This displays the
seller’s profit. It is equal to the revenue minus the total
cost which is the sum of the administrative cost and
the manufacturing cost. The details of calculating the
profit given αare provided in Appendix B.
Past results (Area A19:I40). The competitive aspect
of classroom games can be a significant motivating fac-
tor for keeping the students engaged (Miyaoka 2005).
To allow the students to compare their performances to
those of all the AI sellers throughout the BucknellAuto
game, the bidding history appears in C20:I40. The cells
below A19 show what the AI sellers would have bid
given the student’s total cost. The [Reset records] but-
ton clears any historical data thus far. Figure 7shows
the game results at the end of the 20 auctions.
We offer a two-player game for the instructor who
wants to assign the students in pairs to compete with
each other. No additional software or hardware would
be needed compared to the single-player game because
the two players will be sharing the same computer
screen. Figure 8shows the game interface when choos-
ing to play the game in the two-player mode. This inter-
face functions almost identically to the single-player
game interface. The only procedural difference is that
the students take turns entering the bids while the
other student is looking away. Because the two play-
ers would have the same total manufacturing cost, a
sealed-bid setting makes sellers’ collusion less likely.
Next, we provide a guide and recommendations for
using the BucknellAuto game in the classroom.
2.3. Game Development
The BucknellAuto game can be conducted in four
phases.
2.3.1. Phase 1. Before the game begins, the students
gain understanding of the RA by relating it to the
well known forward auction, Sotheby’s, since the auc-
tion participants’ roles and responsibilities in the two
types of auction are completely opposite. The instruc-
tor may spend some time educating the students about
the core concepts of the first-price auction type used by
the game. The goal of this session is to familiarize the
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Chen and Bailey: The BucknellAuto Game
122 INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s)
Figure 7. Reverse Auction Results
students with the general structure of the RA. In our
experience, this may take about 15 minutes.
2.3.2. Phase 2. After the introduction, students
should freely play a few auctions to familiarize them-
selves with the game operations (the Excel Solver Add-
in must be enabled when opening the spreadsheet file,
otherwise the game will not function). The instructor
should remind the students of three things: (i) The total
cost to their company is the random manufacturing
cost less than $100 plus the administrative cost. (ii) Bid-
ding $0 signifies they want to drop out of the current
auction. (iii) The objective is to maximize the average
profit and win at least three auctions. Essentially, the two
implicit objectives, i.e., average profit and percent of
the auctions won, require different bidding strategies.
If time permits, the instructor may single out one objec-
tive or adjust the required number of actions won to
let students discover the appropriate bidding strategy
during game play. We think the fun of the game can
be augmented if different objectives and different bid-
ding strategies are tried. This session may take about
ten minutes. Students should then be ready to play the
game. At the end, every student should click the [Reset
Records] button to clear all the trial results thus far
before proceeding to the next phase.
2.3.3. Phase 3. Before the competition officially starts,
the instructor announces the auction parameter val-
ues and initiates the BucknellAuto game. To effectively
use class time, the instructor focuses on highlighting
some, but not all, of the auction parameters. For exam-
ple, the default beginning auction parameter setting is
three sellers, low administrative cost, slightly conser-
vative risk attitude, and winner takes all auction (N3,
K$10,β0.6, and α100%, respectively). At the end
of the 20 auctions, the instructor can list the students’
average profits and the percentage of auctions won
on the blackboard, and the students themselves can
compare their results to the AI sellers’ results. If time
permits, the instructor should let the students play a
second round using N5. At the end of this round,
the students can compare their average profits and the
percentage of auctions won between the two rounds.
We recommend students play at least two rounds of
the BucknellAuto game using different parameter val-
ues to experience how the game variables can affect the
bidding intensity. In our experience, each round takes
about seven minutes to complete.
2.3.4. Phase 4. After the game, the instructor should
facilitate discussion to augment the students’ learning
experience. Sample questions are as follows:
1. In general, how do you feel about bidding in an
RA as a seller?
2. Did your bidding strategies differ between the
two rounds of auctions? If so, how did the parameter
values affect your bidding behavior?
3. How could using an RA affect the buyer-seller
relationship? How much do you agree that RA is an
effective tool for discovering the true market value of
the item?
Within the RA construct, it is possible to result in a
win-win situation for the buyer and seller. For exam-
ple, non-incumbent sellers can benefit from the RA in
terms of gaining access to new customers, and sellers
can examine their competitiveness by benchmarking
the bids (Kumar and Maher 2008). Thus, the discus-
sion gives the instructor an opportunity to balance any
potentially biased viewpoints. This session may take
about ten minutes. On a side note, the instructor may
consider awarding the students who have the highest
objective values (the average profit and/or the percent-
age of auctions won) to enhance the competitive aspect
of the game.
2.3.5. Extended Discussions. While the primary
learning objective of the BucknellAuto game is an
introduction to the mechanisms and issues in an RA,
the game can also be used for secondary learning objec-
tives such as learning more about auction types and
utility theory. Depending on available class time, the
instructor may further engage the students with some
advanced discussions.
The core concepts of the first-price and second-price
auction types and their implications for the bidding
rationale could be naturally taught with the Bucknell-
Auto game. The instructor may refer students who
are interested in the bidding strategy of first-price
or second-price auctions to Kagel and Levin (1993),
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Chen and Bailey: The BucknellAuto Game
INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s) 123
Figure 8. Screen-Shot of the Two-Player Reverse Auction Bidding Game
Che (1993), and the listed references. For general un-
derstanding, the instructor may show the risk-neutral,
equilibrium bid predictions for the forward auctions as
shown below, where xdenotes the seller’s private eval-
uation of the item values (Kagel and Levin 1993):
First-price: x(N1)/N
Second-price: x.
Also, Kagel and Levin (1993) provided some inter-
esting statistics: Around 90% of all the bids in the
first-price auction experiments fall below the theoret-
ical prediction, whereas only 4% of all the bids in
the second-price auction experiments fall below the
prediction. We hope playing the game can help stu-
dents relate these bidding strategies via the first-hand
experience.
For students who are interested in the robots’ bid-
ding rationale, the instructor may construct a decision
tree to illustrate the basic idea of the utility theory on
which the AI seller bidding rationale is based. Figure 9
shows that the two identical, risk-averse sellers would
enter the auction if and only if the expected utility of
entering the auction is greater than the expected utility
of not entering the auction:
v(bC+WK)β+(1v)(WK)β>Wβ,
where vis the probability that the seller is the lower
seller than the other, and Wis the seller’s initial wealth.
A numerical example would also be helpful for the
students’ understanding. Consider two identical risk-
averse sellers (β0.6) that place random bidding prices
above the manufacturing cost (v0.5). The sellers
face two options in a reverse auction: To bid or not
to bid? Without loss of generality, we assume the sell-
ers have an initial wealth equal to the administrative
cost (WK) so that entering the auction is an option.
Suppose the total manufacturing costs are $50 and the
administrative costs are $10 (identical sellers). As a
result, the bidding price must be greater than $81.75
if the sellers decided to enter the auction. If the two
sellers are not identical with respect to the distribu-
tion of the random bidding prices (v,0.5), then the
seller who aims at earning $25 as profit would not bid
unless her winning probability vis at least 0.58. Note
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Chen and Bailey: The BucknellAuto Game
124 INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s)
Figure 9. Simplified Example of How the AI Seller Decides Whether to Enter the Auction
Utility
Lower bidder
with probability of v
Revenue: b
Manufacturing cost: C
(b C + W K)^
Higher bidder
with probability of (1 – v)
Revenue: 0
Manufacturing cost: 0
(W K)^
Decision
Initial wealth: W
Not entering auction
Admin. cost: 0
W^
Robots bidding strategy:
Two identical risk-averse ( < 1) bidders,
winner-takes-all setting ( = 1)
Entering auction
Admin. cost: KEvent
that the solutions can be easily obtained by the func-
tion of “Goal-Seek” in Excel. The instructor may prefer
to offer these relatively straightforward utility calcula-
tions as assignments, exercises or homework problems
after the exercise.
2.4. Game Limitations
To focus on the core factors in an RA for students, we
have streamlined the complex RA structure to a sim-
ple game that can be played quickly and repeatedly.
Inevitably, the BucknellAuto game cannot fully reflect
reality due to its limitations. Issues that can be dis-
cussed in a wrap-up discussion are:
Single bid: Only a single bid is permitted per auc-
tion item per seller, but in practice buyers can oper-
ate the bidding process in stages. In this scenario, the
buyer manages a series of bids from each seller in the
hope of further lowering the accepted price (Emiliani
and Stec 2002).
Price-only auction: The BucknellAuto game as-
sumes a price-only auction, but in practice the buy-
ers can consider other seller attributes such as capac-
ity, quality or lead time when determining the auction
winners (Talluri and Ragatz 2004, Teich et al. 2005).
Seller assessment: In practice, participating sellers
in the RA must quote the auction item based on the
same item material and manufacturing specifications
requested by the buyer. The buyer would be wary of
any abnormally low bidding price in case the seller
is gaining a cost advantage over competitors by not
adhering to these specifications. In the BucknellAuto
game, a very low manufacturing cost would not dis-
qualify the seller from participation.
Incumbent seller: In practice, the buyer may use
the incumbent seller to fulfill the demand request if
no sellers participate (Kumar and Maher 2008). In the
BucknellAuto game, we assume that, if no seller partic-
ipates, then the buyer will clear the need for the current
auction using an external source.
3. Effectiveness Evaluation
To evaluate the BucknellAuto game effectiveness, we
have designed a student survey with five quantitative
questions and one qualitative question requesting gen-
eral feedback (Ashenbaum 2010). The undergraduate
students from the Quantitative Reasoning for Man-
agers (first- and second-year students) or Global Sup-
ply Chain Management (third- and fourth-year stu-
dents) courses participated to the game. The students
answered the questions before and after participating
in the game. The following statistics are based on 109
surveys collected.
In the survey, the first three multiple-choice ques-
tions were an attempt to reveal the students’ explicit
understanding of the facts and purposes of reverse auc-
tions. We found that the students have significantly
improved their knowledge about reverse auctions after
playing our game. The fourth and fifth survey ques-
tions focused on the students’ overall understanding
of reverse auctions and their comfort in explaining a
reverse auction to someone else. The survey questions
are as follows:
Q1. A reverse auction is typically conducted with
the following participants:
(1) Multiple buyers, multiple suppliers.
(2) Multiple buyers, single supplier.
(3) Single buyer, multiple suppliers.
(4) Single buyer, single supplier.
Q2. In a reverse auction, the bidding prices
tend to
(1) increase, in favor of the suppliers.
(2) increase, in favor of the buyer.
(3) decrease, in favor of the suppliers.
(4) decrease, in favor of the buyer.
Q3. A reverse auction is a tool for discovering the
true _______ of the auctioned subject.
(1) Quality.
(2) Service.
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Chen and Bailey: The BucknellAuto Game
INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s) 125
Table 1. Game Effectiveness Evaluation
Correct rate Q1 (%) Q2 (%) Q3 (%) Q4 Q5
Before game 76.15 57.80 83.49 1.97 1.93
After game 97.25 91.74 94.50 6.27 6.31
(3) Market price.
(4) Delivery time.
For Q4 and Q5, please use a number between 1 and 7,
where 1 is strongly disagree and 7 is strongly agree, to
answer the questions.
Q4. I feel that I have a big picture understanding of
reverse auctions.
Q5. I could describe the basics of how a reverse auc-
tion works.
Q6. General comments.
We note that any missing or illegible answers in the
collected surveys were treated as incorrect. We found
significant statistical evidence showing that the game
can effectively achieve its primary purpose. Table 1
shows the pregame and postgame survey statistics. The
tests of equal proportions for the first three questions
and the tests of equal means for the last two ques-
tions rejected the hypotheses that the pregame and
postgame results are equal (Q3 results are significant
with a p-value 0.0173; all the other question results
are significant with p<0.0001).
Finally, we offered a sample of representative com-
ments from the last survey question:
I have learned what a reverse auction is and how com-
petitive it is to be a seller in a reverse auction. The exercise
helped me put reverse auctions in a real-life experience to
really learn how it works.
From the exercise, I learned that it is difficult to find a
balance between bidding low to attract business and bidding
high to keep a profit margin. This exercise helped me learn
that reverse auctions are very competitive from the seller’s
point of view.
By doing the game, I experienced first-hand the influ-
ence of multiple sellers on my bidding decisions as well as
the overall profit flow of the auction. The decision-making
skills and thinking that went into the game let me clearly see
the advantages and the disadvantages of such an auction.
I really liked this exercise! I learned that it is important
in a reverse auction to bid low enough that you will win,
but high enough that you will have a profit. It was also
interesting to look at the averages at the end!
The simulation was very helpful. It forced you to try
to think like the competitors to a point where you had a
good idea in what they were going to bid. By adding the
additional sellers, you felt increased level of pressure where
you were afraid to bid too high and became greedy when your
manufacturing cost were low, and it steered you away from
bidding when your costs were mid to high.
Based on our experiences with the BucknellAuto
game and the data above, we believe the game effi-
ciently and effectively helps an instructor augment the
student’s RA learning experience and transform the
lecture session into a fun and interactive activity.
4. Conclusion
The prevalence of RAs in academic research and
in practice motivated us to introduce RAs to our
undergraduate business majors. This paper presents a
spreadsheet-based RA bidding game in which students
assume the seller role and vie for the buyer’s business by
bidding against a number of automated AI sellers. The
BucknellAuto game allows students to logically think
through the practical trade-off between winning the
auctions and making profits when bidding. In our expe-
rience, this experimental learning game improved the
student’s understanding of the basis of RA. We believe
the BucknellAuto game can help operations research
or management science instructors better engage the
students in teaching the fundamental concepts of RA,
and transforming the conventional RA lecture into a
fun and interactive session. While our primary goal was
to provide an introduction to and illustration of RAs
for undergraduate business majors, the BucknellAuto
game could also be used to complement more technical
instruction on supply chains including more detailed
methodological instruction on topics such as auction
design, utility theory, and game theory.
Acknowledgments
We thank the referees, associate editor, and editor for the
various excellent suggestions in improving this manuscript.
We also thank Dr. Christine Kydd for her valuable feedback
for improving the paper. All errors are the responsibility of
the authors.
Appendix A. Seller Bidding Rationale
In the game, the automated sellers’ bidding behavior is gov-
erned by a bidding function using the auction parameters to
generate each seller’s bid. See Klotz and Chatterjee (1995) for
more details. Here we present only some key points of the AI
sellers’ bidding rationale.
Basically, the robots will enter the auction if and only if
the expected utility associated with entering is at least as
large as the expected utility of not entering: (We suppress the
subscript ifor ease of disposition)
Pr(Cis lowest)Ɛ[U(winning |Clowest)]
+Pr(Cis second lowest)Ɛ[U(winning |Csecond lowest)]
+Pr(Cis greater than second lowest)
·Ɛ[U(not winning |Cis greater than second lowest)]
U(not entering the auction at all).
Given the auction parameter values, one may solve the drop-
out manufacturing cost, e.g., C, from this inequality. The
robots then use Cto decide whether to enter the auction.
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Chen and Bailey: The BucknellAuto Game
126 INFORMS Transactions on Education, 2018, vol. 18, no. 2, pp. 116–126, ©2017 The Author(s)
For example, if the total manufacturing cost for an auction
item, C, is greater than the drop-out cost, C, then the seller’s
expected utility of entering the auction would be less than
the utility of not entering the auction, prompting the seller
to drop out of the auction by bidding zero. If entering the
auction, the robots then calculate the equilibrium bidding
price which is a function of C,K,N,β,αand involves some
integration requiring a separate worksheet in the game file to
numerically approximate the results.
Appendix B. Bidding Profit Calculations
For a given auction:
(i) The sellers who decide not to participate by bidding
zero incur no profit nor loss.
(ii) The seller with the lowest bcalculates the profit using
the following formula:
αbαC+K.
(iii) The seller with the second lowest bcalculates the
profit using the following formula:
(1α)b− (1α)C+K.
(iv) The other sellers have the profit as:
K.
Note that in a dual-sourcing setting, if there is only one
winner, then the winner takes the entire demand quantity
instead of α.
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