How to Use Data Science in Economics – a Classroom Game Based on Cartel
Detection

Hannes Wallimann and Silvio Sticher

University of Applied Sciences and Arts Lucerne, Institute of Tourism and
Mobility

Version January 2024

Abstract: We present a classroom game that integrates economics and data-
science competencies. In the first two parts of the game, participants assume
the roles of firms in a procurement market, where they must either adopt
competitive behaviors or have the option to engage in collusion. Success in
these parts hinges on their comprehension of market dynamics. In the third
part of the game, participants transition to the role of competition-authority
members. Drawing from recent literature on machine-learning-based cartel
detection, they analyze the bids for patterns indicative of collusive (cartel)
behavior. In this part of the game, success depends on data-science skills. We
offer a detailed discussion on implementing the game, emphasizing
considerations for accommodating diverging levels of preexisting knowledge in
data science.

Keywords: data science, economics, classroom games, cartel detection

Addresses for correspondence: Hannes Wallimann, University of Applied Sciences
and Arts Lucerne, Rösslimatte 48, 6002 Lucerne<EMAIL_ADDRESS>Silvio Sticher<EMAIL_ADDRESS>
##  1 Introduction

Ever since the advent of game theory in the mid-20th century and George
Stigler’s "The Theory of Oligopoly" (Stigler, 1964), the study of cartels has
been an integral component of any economics curriculum. Cartels, which cause
prices to increase and/or the quality of products and services to decrease,
not only intrigue researchers but are of utmost importance to policymakers,
who have to make sure that public funds are used in an efficient manner.
Moreover, cartel formation is illegal in most countries worldwide, and firms
must expect high sanctions when a conspiracy is detected.

In recent years, the erstwhile predominantly theoretic field of industrial
organization has gradually shifted towards empirical research. One
contributing factor is the increasing potential to harness large data sets for
scrutinizing markets and identifying patterns indicative of cartel presence
(see, e.g., Harrington, 2008), an indispensable first step in fighting
cartels. According to the OECD (2022), in the past years, the literature on
cartel screening has primarily focused on the utilization of machine learning.

From the students’ and practitioners’ point of view, such developments pose a
challenge, as modern data-science skills are suddenly required in addition to
understanding (imperfect) markets. The added complexity may hinder their
ability to translate motivation into action, a gap that educationalists
sometimes propose narrowing through the use of "edutainment" (see, e.g.,
Prensky, 2003). As Alsawaier (2018) summarizes, this can be achieved either by
adding game elements and mechanics to the educational environment
("gamification") or by simulating content using actual games ("game-based
learning"). We follow the second approach by incorporating a game with defined
learning outcomes (Plass, Homer, and Kinzer, 2015), following the argument
games motivate learners to stay engaged over a long period through a series of
motivational game features. However, we also consider Folmar’s cautionary
note, who argues that classroom games carry the risk of short-lived engagement
and motivation, ending with the game (Folmar, 2015). To address this, we break
the game into several parts and integrate it with other teaching elements,
such as theory inputs.

The learning objectives of our classroom game are that participants gain an
understanding of how data science is employed in cartel detection and that
they are able to utilize corresponding tools accordingly. The virtual setting
of our classroom game is the procurement procedure in the construction sector.
In public-sector contracting, procurement agencies invite firms to submit bids
for projects put to tender (for Switzerland, see, e.g., Wallimann, Imhof, and
Huber, 2022). Therefore, a procurement agency announces future contracts and
deadlines for bid submissions. Moreover, the agency provides interested firms
with relevant information for the contract. Then—if interested—construction
firms prepare and submit their bids. After a pre-announced date, the
procurement agency proceeds with a detailed examination of the firms’ bids.
When it comes to awarding contracts, an array of criteria come into play,
encompassing references, quality, environmental considerations, and more.
Among these, the pivotal criterion, especially in the field of road
construction (and civil engineering in general), pertains to the offered price
(or bid). The thing to notice is that in some markets, there exist traits
conducive to cartel formation (Harrington, 2006) whereby firms conspire to
raise prices (or lower the quality of goods and services). Collusion is more
likely with a small number of firms, little or no entry, repetitive bidding,
and stable demand (see, e.g., Ken Danger, 2009). As a result, the construction
industry is particularly prone to collusion and is therefore chosen as our
field of application.

In the first two parts of our classroom game, participants take on the role of
construction companies that can collude—or not—by submitting bids for projects
put to tender. They can earn victory points as an analogy to the profits that
firms obtain, both lawfully and illicitly. In the final part of the game, they
take on the role of staff members within an antitrust authority applying
machine learning algorithms in order to flag cartels. In this sequence,
participants’ victory points are modified depending on their success in
applying the relevant data-science techniques, drawing an analogy to the
recognition and career opportunities for antitrust professionals. Depending on
the requirement level of the course or training sequence, this can involve
sophisticated approaches, such as training models and selecting algorithms, or
more accessible options, including purely visual analysis.

The rest of our paper is organized as follows. In Section 2, we offer a
concise summary of the relevant literature. In Section 3, we specify the
classroom game by describing the setting and parameters, along with detailing
the game mechanics. This includes the bidding and awarding procedure of the
first two parts of the game and the cartel-flagging mechanism of the final
part. To support lecturers, we also provide an illustrative example on how to
compute victory points. In Section 4, we discuss the implementation of the
classroom game in different settings with an emphasis on skill requirements.
We conclude in Section 5, and provide supporting teaching material in the
Appendix.

##  2 Related literature

Our proposed classroom game relates both to recent advances in cartel
detection as well as game-based learning in economics.

As stated in the introduction, our game is situated within the evolving
landscape of economists’ tasks, particularly the increasing integration of
machine-learning techniques for detecting cartel behavior. This topic has
aroused the interest of economists in resent years (see, e.g., Varian, 2014,
Athey and Imbens, 2019). Harrington’s insights (Harrington, 2006), which
suggest that the construction sector is particularly susceptible to collusion,
have been confirmed on several occasions (see, e.g., Bergman, Lundberg,
Lundberg, and Stake, 2020, Imhof, Karagök, and Rutz, 2018, Ishii, 2014, for
examples from Sweden, Switzerland, and Japan, respectively). The use of
statistical methods to screen markets to detect patterns of a cartel was
proposed, among others, by Porter and Zona (1993) and Harrington (2008).
Following many machine-learning applications (see, e.g., Imhof and Wallimann,
2021, Harrington and Imhof, 2022, Huber and Imhof, 2019, Rodríguez, Rodríguez-
Montequín, Ballesteros-Pérez, Love, and Signor, 2022, Silveira, Vasconcelos,
Resende, and Cajueiro, 2022), we also use behavioral screens as predictors in
supervised models to detect collusive behavior.

Game-based learning and classroom experiments are increasingly attracting
attention in economics education (Holt, 1999, Picault, 2019, Platz, 2022). An
example is the paper of Dobrescu, Greiner, and Motta (2015), assessing and
discussing a video game in a standard Microeconomics introductory
undergraduate course. Another example is the Chair the Fed online simulation.
This video game, developed by the Federal Reserve Bank of San Francisco and
discussed by, e.g., Duzhak, Hoff, and Lopus (2021), teaches on the Fed’s dual-
mandate goals of stable prices and low unemployment. A closely related study
to our proposal is presented by Correa, García-Quero, and Ortega-Ortega
(2016), which employs a role-play scenario to teach the strategic behavior of
a cartel, with participants acting as member countries of the Organization of
Petroleum Exporting Countries (OPEC). Additionally, Picault (2015) introduces
a classroom experiment to assess strategic interactions and collusion among
producers in a market.

##  3 Classroom game

The classroom game is divided into three parts. Participants act as
construction firms submitting bids to a procurement agency in the first two
parts. In Part 1, they act as an oligopoly, with no coordination allowed. That
is, they submit bids based on the known distribution of costs as well as on
the known value of their own cost. In Part 2, this procedure is repeated, with
the difference that explicit coordination among each other is now allowed. In
Part 3, the participants switch sides and apply their data science and
economics knowledge to flag conspiracies by taking on the role of employees of
an antitrust authority. In the following, we will use the term "firms" to
denote participants in Parts 1 and 2 and "employees" to refer to them in Part
3. Other roles of the classroom game, such as the procurement agencies and the
antitrust authority’s board of directors, remain unallocated to participants.
Instead, these roles adhere to the game’s rule set, overseen by the lecturer.
Figure 1 illustrates the classroom game’s action. In Appendix A, we suggest a
suitable groups allocations depending on the class size.

Figure 1: Parts of the classroom game

In the following, we first explain the setting in greater detail. Second, we
show how firms calculate their costs for a single project (being relevant in
Parts 1 and 2). Next, we explain the bidding and the awarding procedure of
Parts 1 and 2. Fourth, we explain the machine learning application to screen
for cartels in greater detail (Part 3). Finally, we present a concluding
example.

###  3.1 Setting

Revisiting Figure 1, we observe that Parts 1 and 2 each contain four years,
and each year contains four projects put to tender by a procurement agency.
The mentioned procurement agency pertains to the fictional region of
"Tetravale" (see Figure 2). Each year, the project locations of the four
tenders are "North Village", "East Village", "South Village", and "West
Village". All participants are divided into groups of three or
four—represented by the four game pieces in Figure 1. Accordingly, firms apply
for all projects at every location.

Figure 2: The fictional region of Tetravale

###  3.2 Calculation of the costs (Parts 1 and 2)

For each project, firms know their costs while bidding. The first cost
component is "fixed costs", which range from 50 to 100. Fixed costs are
different for each tender but the same for all firms. However, three
superimposed factors also influence the firms’ costs.

The first factor is the geographical location of the firm. As the distance
between a firm’s location and the place of the planned construction site
increases, the firm’s cost also increases. As an example, consider the
procurement of a construction site in North Village. East Village’s Firm 2 is
located 5 km apart (cp. Figure 2). Accordingly, we assume that Firm 2’s cost
to fulfill the contract in question increases by 5 percentage points of the
fixed costs, as we record in Table 1. In comparison, South Village’s Firm 3 is
located 15 km from the construction site, which increases its total costs by a
hefty 15 percentage points of the fixed costs. The upper third of Table 1
shows all cost increases owing to the distance between a firm’s and the
construction site’s location.

Table 1: Cost increase in percent relative to the fix costs

|  Firm 1 (North Village) |  Firm 2 (East Village) |  Firm 3 (South Village) |  Firm 4 (West Village)
---|---|---|---|---
Tender in |  |  |  |
North Village | 0 | 5 | 15 | 10
East Village | 5 | 0 | 10 | 15
South Village | 15 | 10 | 0 | 5
West Village | 10 | 15 | 5 | 0
Capacity utilization |  |  |  |
Situation A | 0 | 1 | 2 | 3
Situation B | 3 | 0 | 1 | 2
Situation C | 2 | 3 | 0 | 1
Situation D | 1 | 2 | 3 | 0
Type of contract |  |  |  |
Road construction | 0 | 2 | 4 | 6
Railway track construction | 2 | 0 | 6 | 4
Bus station construction | 4 | 6 | 0 | 2
Civil engineering | 6 | 4 | 2 | 0

Note: Each year contains four tenders, i.e., four rounds.

The second cost-driving factor is capacity utilization, which can be
influenced by factors such as projects from private clients. Within our
classroom game, we simulate dynamic fluctuations in capacity utilization
across rounds. Firms experiencing high capacity utilization, e.g., Firm 4 in
Situation A (see Table 1), can only implement the project at increased costs.
The rationale behind this is twofold. First, working at full capacity
necessitates the temporary hiring of additional personnel, resulting in
administrative obligations. Second, the cost increase can also be attributed
to implicit expenses (opportunity costs). In certain scenarios, the assumption
of a contract may lead to postponing potentially lucrative projects.

In reality, firms’ bidding behavior is influenced by many criteria. These
encompass non-monetary elements such as the inclination to engage in projects
with societal and environmental aspirations. Additionally, there may be long-
term considerations, such as evaluating a project’s impact on the firm’s
portfolio and reputation. For simplicity, we distill these multifaceted
considerations into simple proxies in the shape of additional firm-specific
cost increases. Consistent with existing literature (see, e.g., Wallimann,
Imhof, and Huber, 2022), we assume comparatively small differentials in the
firms’ evaluations of these factors. To illustrate this point in the classroom
game, we introduce a third influencing factor. We assume the existence of four
distinct project types: "road construction", "railway track construction",
"bus station construction", and "civil engineering". Each firm is specialized
or at least inclined towards the execution of a specific type. As exemplified
by Table 1, when a road-construction project is put up for tender, the costs
of Firms 1, 2, 3, and 4 experience increases of 0, 2, 4, and 6 percentage
points, respectively, over their fixed costs.

To summarize, let us consider an example regarding Firm 1, situated in North
Village: In Round 1, the procurement agency of West Village is tendering for
the construction of new tracks (railway track construction), Firm 1’s capacity
utilization is low (Situation A), and all firms’ fixed costs are 100. The
costs of Firm 1 amount to $100\times(1+0.1+0+0.02)=112$. Next, in Round 2, the
procurement agency of East Village puts a civil-engineering project to tender,
Firm 1’s capacity utilization is higher (Situation $C$), and all firms’ fixed
costs are 75. In this case, the costs of Firm 1 amount to
$75\times(1+0.05+0.02+0.06)=84.75$ (see Table 1).

As implied by this example, the combination of a project’s location, a firm’s
capacity utilization, and the type of the contract are introduced with an
element of randomness. Throughout the progression of the four rounds,
competitiveness is balanced across all participating firms (whether there are
three or four firms associated with the tender, confer to Table A.1 Appendix
A). Note, however, that instances may arise where a firm’s competitive
advantages or disadvantages concentrate within specific scenarios.

###  3.3 Bidding and awarding procedure (Parts 1 and 2)

Each year, the firms simultaneously receive tenders for four projects. They
prepare and submit their bids, drawing upon their self-calculated cost
structures as well as their expectations of competitors’ actions. Enabling a
dynamic, albeit tacit, interaction, the firms receive information about the
allocation of contracts, as detailed out below. This process repeats four
times in both Part 1 and Part 2. In Part 1 of the classroom game, the
participants are not allowed to communicate with each other, while in Part 2,
they get an opportunity to talk to each other before bidding. However, they
are advised to be careful when doing so: The digital trail they leave behind
could raise red flags with the antitrust authority. Without going into
specifics, the firms are informed that such circumstances could necessitate
the reimbursement of profits derived from the implicated tender.

Following each year (encompassing each four tenders) in Parts 1 and 2, the
procurement agencies allocate contracts to firms with the lowest bids and
inform them accordingly. All participants are informed about the winner
(player) but not the winner’s bid. Additionally, the winner is notified on the
profit margin, computed as the difference between his or her cost and bid.
This margin is directly translated to victory points. Firms that do not secure
contracts receive zero victory points. Note that in the tenders of Part 2, the
awarding of victory points is of a temporary nature, as detailed below. The
point-assignment process applies across all 32 tenders within each group (four
tenders per year and four years per part over the course of two parts).

###  3.4 Flagging cartels (Part 3)

In the final part of the classroom game, participants take on the role of
staff members within the antitrust authority tasked with overseeing
Tetravale’s markets. They comprehensively evaluate the pooled tenders
presented in Parts 1 and 2, scrutinizing them for potential cartel activities.
Then, they advise their board of directors to decide which cases merit more
in-depth investigations. As we explain below, successful advice leads to
recognition, later converted into victory points.

To clarify the awarding process, note that after the screening of tenders
(which can be done as a homework assignment in more advanced classes or as an
in-class activity in less detailed courses), each employee classifies each
tender as either “suspicious” or “non-suspicious”. To do so, the antitrust
authority arranges the tenders in a random way. By applying code as provided
in the example in Appendix C, the employees are then able to prepare a data
set with every tender as an observation containing an ID variable and the
screens as predictors in separate columns of the data set. As a result of the
rearrangement of the tenders, employees can no longer (or, at least, hardly)
recognize their own tenders from Parts 1 (actual value non-suspicious) and 2
(actual value suspicious). Next, they, can develop their machine-learning-
based codes. To this end, following Wallimann and Sticher (2023), the
antitrust authority provides the employees with data from the three cartels
from Switzerland See-Gaster, Grisons, and Ticino, previously also introduced
by Imhof, Karagök, and Rutz (2018) and Wallimann, Imhof, and Huber (2022).

Based on this data, the participants estimate their models. Depending on their
level of data-science knowledge, prepared code can be distributed or
participants may the freedom to choose algorithms and code (see Section 4). In
the baseline proposal of our classroom experiment, we suggest an analysis
using ready-made "screens". Screens are descriptive statistics of bids
describing bidders’ behavior in a tender. As predictors for our binary outcome
variable—which takes on the value 1 when firms collude and the value 0 when
they compete—, we use the coefficient of variation (CV), the spread (SPD), the
difference between the two lowest bids (DIFFP), the relative distance (RD),
and the normalized distance (NORMRD). We formally introduce the screens in
Appendix B. Applying such screens, participants should be enabled to capture
distributional changes due to a cartel’s coordination of bids. Having
developed their models, the participants now classify the tenders of Parts 1
and 2 as suspicious or non-suspicious.

The incentives for the participants are as follows: In Part 3, no additional
victory points can be accrued. Instead, the points obtained in Parts 1 and 2
are considered and modified to determine the winner over the course of the
three parts. As members of the antitrust authority, the participants’ primary
goal is to accurately classify as many tenders as possible. Therefore, to
determine the winner of the competition, only participants in the top half of
Part 3 are considered. Specifically, to be eligible to win, a participant’s
"correct-classification rate" (comprising true-positive and true-negative
classifications) must meet or surpass the median of the correct-classification
rate of the class.

Furthermore, to address the significance of false-positive accusations, which
the antitrust authority aims to minimize for reputational reasons (also in
light of the heavy legal consequences of a firm being flagged as a potential
cartel participant), each incorrect labeling of a "suspicious tender" results
in a 5% reduction of the a participant’s victory points.

Before this deduction takes place, it is important to note that the points
awarded in Part 2 are provisional: Once at least 75% of the antitrust
authority’s staff members classify a tender as suspicous, it is deemed
"unequivocal suspicious". This initiates a more extensive investigation,
including key-witness interviews and raids, to provide a vivid illustration.
In cases where a tender was actually a cartel (i.e., a tender of Part 2), the
victory points provisionally awarded in Part 2 are revoked.

###  3.5 Concluding example

The classroom game concludes with the unveiling of the victory point
progression. As an illustration, consider a scenario involving a class
composed of twelve participants, leading to the formation of three groups,
each comprising four firms. Focus on Participant $A$’s firm and its markups
during the four years of competition and collusion, respectively:

Competition (Part 1):
$\displaystyle\\{\overbrace{(0,0,0,0)}^{\shortstack{\scriptsize Part 1, \\\
\scriptsize Year 1}},\overbrace{(0,0,0,0)}^{\shortstack{\scriptsize Part 1,
\\\ \scriptsize Year 2}},\overbrace{(10,10,0,0)}^{\shortstack{\scriptsize Part
1, \\\ \scriptsize Year 3}},\overbrace{(0,0,0,3.5)}^{\shortstack{\scriptsize
Part 1, \\\ \scriptsize Year 4}}\\},$ Collusion (Part 2):
$\displaystyle\\{\underbrace{(0,0,10,0)}_{\shortstack{\scriptsize Part 2, \\\
\scriptsize Year 1}},\underbrace{(0,0,10,0)}_{\shortstack{\scriptsize Part 2,
\\\ \scriptsize Year 2}},\underbrace{(0,20,0,0)}_{\shortstack{\scriptsize Part
2, \\\ \scriptsize Year 3}},\underbrace{(0,20,0,0)}_{\shortstack{\scriptsize
Part 2, \\\ \scriptsize Year 4}}\\}.$

In Part 1, Participant $A$ accumulates 23.5 victory points. This includes two
markups of size 10 in Year 3 and one markup of 3.5 in Year 4. Likewise, $A$
secures 60 victory points from Part 2, but it is essential to understand that
these points are provisional, given the impending investigation in Part 3.

Switching sides in Part 3, all participants submit their lists of suspicious
and non-suspicious tenders. The antitrust authority subsequently scrutinizes
all tenders classified as suspicious by at least 75% of the participants. In
this context, assume that all tenders within Years 3 and 4 of Participant
$A$’s group fall within this category of unequivocal suspicious tenders.
Consequently, $A$ forfeits 40 of the 60 victory points gained in Part 2.

Before considering her performance as a staff member of the antitrust
authority, $A$’s vicotry points total $23.5+(60-40)=43.5$.

Now, assume that $A$ also ranks among the top half of the class in terms of
the correct-classification rate in Round 3. Furthermore, suppose that she
mistakenly labels eight competitive tenders from Round 1 as suspicious. In
this case, $A$ remains eligible to win but experiences a 40% reduction of her
victory points, corresponding to the eight incorrect classifications at 5%
each.

In total, across Parts 1 to 3, Participant $A$ accrues $43.5\times 60\%=26.1$
victory points, positioning her as a contender for the main prize, as
predetermined by the lecturer. We recommend considering a symbolic prize,
perhaps a luncheon voucher, to underscore the intrinsic motivation associated
with winning the game.

##  4 Didactic recommendations

The integration of machine-learning techniques will become increasingly
important in social sciences in the future. The research on cartel screening
serves as a typical example of this trend. This shift in research methods
presents challenges for both students and practitioners, as individuals may
excel in either economics or data science but less frequently in both. Our
classroom game serves as an example of how social-science educators can
incorporate the interdisciplinary nature of modern economics into the
classroom without overstraining the participants’ capacities. More generally,
it demonstrates how scientific articles can be taught in an application-
oriented manner.

In the following, we discuss our findings from an initial in-class
realization. Thereupon, we summarize considerations for implementation,
emphasizing different settings, participant compositions, and states of
knowledge, respectively. The appendices in this paper also provide further
basic information on how teaching materials can be designed.

###  4.1 Insights from an initial implementation

The working-paper version of this article will be published before an initial
implementation will have taken place.

Note that the classroom game will be provided as an interactive tool in the
.xlsm format (Microsoft Excel documents with macros). This tool facilitates
interactions between participants and the lecturer and automates computations
associated with "non-playable characters," such as procurement agencies and
the antitrust authority. Please note that these files, along with related
instructions, are not published in connection with the working-paper version
of this article. Extensive playtesting in class must occur first.

###  4.2 Recommendations based on data-science knowledge

One challenge of embedding data science in (economics) lessons is the question
of the participants’ knowledge of data science and machine learning. We
categorize participants with respect to their knowledge according to three
groups:

  1. i.

Participants with advanced data-science knowledge,

  2. ii.

participants with basic data-science knowledge,

  3. iii.

participants with no (or hardly any) data-science knowledge.

Participants from the advanced group can train models themselves using
algorithms and statistical markers of their choice. In instances with even
better trained participants, they could even apply unsupervised machine-
learning algorithms (see, e.g., Silveira, de Moraes, Fiuza, and Cajueiro,
2023).

In the second case, i.e., when preexisting knowledge is limited to the basics,
it is advisable to specify specific algorithm-training processes. As an
example, the code in Appendix C demonstrates the application of the random-
forest algorithm. The utilization of predefined code has the advantage that
the analysis can be carried out in the classroom even when time is limited.
However, this approach also has two disadvantages: First, the uncritical
adoption of existing code contributes less to the understanding of the
subject. Second, all participants will obtain identical results. (There are
only deviations if participants use different "random seeds"—or if they make
mistakes). To alleviate these issues, participants can be encouraged to modify
the critical value for the variable "cartel probabilities" (variable
"threshold" in the code of Appendix C). This adjustment influences the random-
forest algorithm’s classification of a bid, indicating the presence of a
cartel. In doing so, participants who recognize that "false positives" can
have particularly severe consequences in the cartel-flagging process (see
Subsection 3.4) have the opportunity to distinguish themselves by classifying
potentially collusive bids more conservatively. As this choice entails the
risk of not achieving a sufficiently high "correct-classification" rate, the
additional degree of freedom introduces an engaging new tradeoff in addition
to gaining a deeper understanding.

Finally, in the third case, i.e., when the group has little or no data-science
knowledge, a practical approach involves visual or benchmark-based screening
(see, e.g., Imhof, 2019). For instance, empirical evidence suggests that
colluding firms often submit bids that are closely aligned (see, e.g., Imhof,
Karagök, and Rutz, 2018). While more advanced groups incorporate this insight
by integrating the statistical markers into the algorithm’s training, the same
pattern can be discerned through visual representations of bid distributions
(utilizing scatterplots) in widely available statistical software like
Microsoft Excel. Also when examining other markers introduced in Appendix B,
conspicuous values can be identified visually: Low values of the coefficient
of variation (CV) link to collusion. The spread (SPD) assumes high values when
the lowest and highest bids diverge substantially. DIFFP represents the
difference between the two lowest bids. The relative distance (RD) and
normalized relative distance (NORMRD) scale the difference between the two
lowest bids relative to the variation of the losing bids and the differences
between any bids, respectively. In class, the lecturer can either present
scientific evidence on these markers or engage students in a discussion about
patterns that may raise suspicion. The subsequent classification within needs
to necessarily involve graphical representations of the bid distribution.
Participants could also classify tenders based solely on the numerical values
of the bids.

Being best equipped to assess the proficiency of their classes themselves,
lecturers have the flexibility to tailor our suggestions to meet the unique
needs of the participants. Even in classes with advanced data-science
knowledge, incorporating visual analysis may prove worthwhile. It not only
acknowledges and rewards participants for their intuitive understanding of the
subject, which may capture nuances in the bids distribution "overlooked" by an
algorithm. The possibility of overwriting machine-learning-based
classifications also introduces greater heterogeneity in the cartel-flagging
process, fostering additional game strategies and thereby adding excitement.

Be aware that introducing the setting, especially in Part 3, may be time-
consuming. While Parts 1 and 2 of the game are intended for in-class play,
Part 3 can be structured as homework assignments. This allows for a brief
discussion of Part 3 during the following class (alongside awarding the
winner). Furthermore, this assignment has the potential to enhance
participants’ competence acquisition, given that the task can be completed at
individual paces.

##  5 Conclusion

In this study, we showcased how game-based learning can be deployed to address
the challenges arising from the multidisciplinary nature of modern economics.
To do so, we presented a classroom game that integrates economic theory with
the application of machine learning. The first two parts involve participants
acting as firms in an oligopoly, submitting bids for construction projects.
Communication is restricted in Part 1 and enabled in Part 2. In the third
part, participants assume the role of employees in a competition authority,
pursuing the goal of detecting illegal collusion in bid patterns. The
classroom game’s design, breaking it into three parts and combining it with
theoretical inputs, addresses concerns about potential short-lived engagement
raised by critics of classroom games. This approach supports the contribution
of the learning objectives in that participants remain motivated throughout
the entire learning experience. Moreover, a focus of our paper lies within
Section 4, where we provide educational suggestions inter alia for groups with
different data science knowledge. Moreover, in the Appendix, we added teaching
material tailored to the classroom game.

Our classroom game serves as a practical and engaging approach to address the
evolving landscape of cartel detection in the context of economics and data-
science education. Through the three parts of our game, participants not only
gain insights into the dynamics of collusion in markets, illustrated by the
construction sector, but also develop skills in utilizing data-science
techniques for cartel detection by examining bid data for suspicious patterns.
As the use of machine learning in cartel screening becomes increasingly
prominent in industrial organization—both in academics and in the professional
world—our classroom game provides a platform for students and practitioners to
acquire relevant skills in this evolving field. Incorporating this classroom
game into (multidisciplinary) economics education can contribute to preparing
the next generation of professionals to be better equipped to address the
challenges posed by cartels in the era of big data.

## References

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Appendices

##  Appendix A Recommended group sizes

For practical purposes, we suggest suitable allocations into groups of 4 and 3
for any class size from 6 to 32. (With even more extensive classes, due to
handling considerations, we recommend splitting up the group into two half
classes and playing the game in two separate sessions. With less than 6
participants, all players could be part of one group.) The rule behind the
recommendations recorded in Table A.1 is to form as many groups of size four
as possible while being able to allocate the remaining participants into
groups of 3. The asymmetry, which results in most situations, leads to a
slightly unequal playing field: Specifically, it is easier to succeed in a
tender when only three instead of four firms are involved. However, as the
groups are put together randomly, this bias only occurs ex-post. Furthermore,
outside of sports, there are barely any games that do not involve luck, at
least to some extent. (Chess as a so-called "perfect information" game is one
of the rare exceptions.) Accordingly, there is no need to discourage lecturers
from playing with unequally-sized groups.

Table A.1: Group recommendations as a function of class size $N$ (preceding
the colon)

6: $2\times 3$ participants |  | 15: $3\times 4$ \+ $1\times 3$ participants |  | 24: $6\times 4$ participants
---|---|---|---|---
7: $1\times 4$ \+ $1\times 3$ participants |  | 16: $4\times 4$ participants |  | 25: $4\times 4$ \+ $3\times 3$ participants
8: $2\times 4$ participants |  | 17: $2\times 4$ \+ $3\times 3$ participants |  | 26: $5\times 4$ \+ $2\times 3$ participants
9: $3\times 3$ participants |  | 18: $3\times 4$ \+ $2\times 3$ participants |  | 27: $6\times 4$ \+ $1\times 3$ participants
10: $1\times 4$ \+ $2\times 3$ participants |  | 19: $4\times 4$ \+ $1\times 3$ participants |  | 28: $7\times 4$ participants
11: $2\times 4$ \+ $1\times 3$ participants |  | 20: $5\times 4$ participants |  | 29: $5\times 4$ \+ $3\times 3$ participants
12: $3\times 4$ participants |  | 21: $3\times 4$ \+ $3\times 3$ participants |  | 30: $6\times 4$ \+ $2\times 3$ participants
13: $1\times 4$ \+ $3\times 3$ participants |  | 22: $4\times 4$ \+ $2\times 3$ participants |  | 31: $7\times 4$ \+ $1\times 3$ participants
14: $2\times 4$ \+ $2\times 3$ participants |  | 23: $5\times 4$ \+ $1\times 3$ participants |  | 32: $8\times 4$ participants

##  Appendix B Formal introduction of the screens

Following Wallimann and Sticher (2023), we formally introduce the screens we
use as predictor variables $X$. $t$ denotes a tender $t$; ${\bar{b}_{t}}$
denotes the mean of all bids in tender $t$; $sd_{t}$ and $sd_{\text{losing
bids},t}$ represent the standard deviations of all bids and the losing bids
(not including the lowest one of tender $t$) respectively; $n_{t}$ denotes the
number of bids submitted in tender $t$; $b_{\max,t}$ is the highest bid of
tender $t$; $b_{i,t}$ is the $i$th bid of tender $t$, ordered from lowest to
highest bid. To calculate the screens we apply the following formulas:

$\text{CV}_{t}=\frac{sd_{t}}{\bar{b}_{t}},$ (B.1) |  $\text{SPD}_{t}=\frac{b_{\max,t}-b_{1,t}}{b_{1,t}},$ (B.2)
---|---
$\text{DIFFP}_{t}=\frac{b_{2,t}-b_{1,t}}{b_{1,t}},$ (B.3) |  $\text{RD}_{t}=\frac{b_{2,t}-b_{1,t}}{sd_{\text{losing bids},t}},$ (B.4)
$\text{RDNOR}_{t}=\frac{b_{2,t}-b_{1,t}}{\frac{1}{n_{t}-1}\sum_{i=1}^{n_{t}-1}(b_{i+1,t}-b_{i,t})}.$ (B.5) |

##  Appendix C Code example

The code for the statistical software R provided below builds upon the output
of the tool that leads through Parts 1 and 2 of the classroom game.

In "Load and prepare data", we install and load the readxl, dplyr,
randomForest, and tidyverse packages for R using the install.packages and
library commands. Then, we load into our R workspace the data of Parts 1 and
2.

In "Prepare screens", we prepare the data by computing the screens discussed
in Subsection 4.2). We propose this part of the code also being provided by
the lecturer to participants of any knowledge level, as programming it in
class is time consuming and does not substantially contribute to the learning
objective of understanding how data science is employed to detect cartel
behavior. Specifically, we prepare the screens (SPD, CV, RD, RDNORM, DIFFP) we
use for screening. In conjunction with the data provided by the classroom-game
tool, we obtain a dataset containing anonymized observations including
screens, bids, and an identifier.

In "Add the bids to the sample", we rank the bids of each tender and add them
to the observation, which now includes the tender (defined by group, year, and
round), screens, bids, and an identifier.

We conclude the data preparation in "Finalize and export data set" before
moving on to the algorithm training. (Thanks to Rodríguez, Rodríguez-
Montequín, Ballesteros-Pérez, Love, and Signor (2022), data on such cartels
are publicly available:
https://www.sciencedirect.com/science/article/pii/S0926580521004982 (accessed
on January 26, 2024).) Moreover, lecturers without access to a suitable
dataset might consider other methods for screening, such as described in
Section 4).

In "Prepare screening", we load into our R workspace the data of the Ticino,
See Gaster, and Grison cartels, where the cartels’ incidence is known (see,
e.g., Wallimann and Sticher, 2023). Using the set.seed command, we make sure
that we get the same results while rerunning the code. Then, we split our data
into training and test sets.

In "Train model", by calling the randomForest command, we first investigate
our model’s performances. To do so, we predict the presence of a cartel in the
test set by using $ to call and create subobjects in R. The thing to notice is
that we make probability predictions in order to set the probability
threshold. Then, by comparing the mean difference between the actual and
predicted outcomes, we can calculate the correct classification rate
(accuracy). Running this R code yields a accuracy of 0.834. Put simply, we
correctly classify 83.4% of the cases in the test set. (Note that other
evaluation metrics, e.g., the F1 score, would be appropriate in cases with
non-balanced data sets. For simplification, we present the accuracy here.)

In "Classifications in Part 3", we apply the trained model ("rf") the prepared
data to classify the tenders. Note that we, again, apply a probability
threshold of 0.5.

Finally, in "Write CSV for submission to lecturer", we conclude the analysis
and export a csv document that can be submitted to the lecturer.

# Load and prepare data
install.packages("readxl"); install.packages("dplyr");
install.packages("tidyverse")
install.packages("randomForest")
library(readxl); library(dplyr); library(tidyverse); library(randomForest)
ds <\- read_excel("/path/to/my/directory/Example.xlsx")
ds <\- ds |> group_by(Part, Year, Round, Group) |> mutate(ID = cur_group_id())
ds <\- ds |>add_count(ID, name = "nbids")

# Prepare screens
ds <\- ds |>group_by(ID) |>mutate(max = max(Bid)) # max
ds <\- ds |>group_by(ID) |>mutate(min = min(Bid)) # min
ds <\- ds |>group_by(ID) |>mutate(SPD = (max-min)/min) # SPD
ds <\- ds |>group_by(ID) |>mutate(mean = mean(Bid)) # mean
ds <\- ds |>group_by(ID) |>mutate(sd = sd(Bid)) # sd
ds <\- ds |>group_by(ID) |>mutate(CV = sd/mean) # CV
ds <\- ds |>arrange(ID,Bid) |>group_by(ID) |> mutate(rank = rank(Bid,
ties.method = "first")) #rank
ds <\- ds |>group_by(ID) |>mutate(secondbid = ifelse(rank==2,Bid,NA)) #
second-lowest bid
ds <\- ds |>group_by(ID) |>fill(secondbid, .direction = "updown") # secondbid
ds <\- ds |>group_by(ID) |>mutate(sd_lb=sd(Bid[rank>1])) # sd loosing bids
ds <\- ds |>group_by(ID) |>mutate(RD = (secondbid-min)/sd_lb) # RD
ds <\- ds |>group_by(ID) |>mutate(nbids =n())
ds <\- ds |>group_by(ID) |>mutate(RDNORM = (secondbid-min)*(nbids-1)/(max-
min)) # RDNORM
ds <\- ds |>group_by(ID) |>mutate(DIFFP = (secondbid-min)/min) # DIFFP

# Add the bids to the sample
ds$Bid_1 <\- ds$min
ds$Bid_2 <\- ds$secondbid
ds <\- ds |>group_by(ID) |>mutate(Bid_3 = ifelse(rank==3,Bid,NA)) # third-
lowest bid
ds <\- ds |>group_by(ID) |>fill(Bid_3, .direction = "updown")
ds <\- ds |>group_by(ID) |>mutate(Bid_4 = ifelse(rank==4,Bid,NA)) # fourth-
lowest bid
ds <\- ds |>group_by(ID) |>fill(Bid_4, .direction = "updown")

# Finalize and export data set for Part 3
Tender <\- ds |>filter(rank==1)
data <\- Tender |>select(ID, SPD,CV,RD,RDNORM,DIFFP,Bid_1,Bid_2,Bid_3,Bid_4)
write.csv(data, "/path/to/my/directory/data_prep.csv", row.names=FALSE)

# Prepare screening (example for participants)
data <\- read.csv("/path/to/my/directory/data.csv", sep=";")
set.seed(123)
train=sample(nrow(data),nrow(data)*0.75)
data.test=data[-train,]
data.train=data[train,]

# Train model
rf <\- randomForest(factor(cartel)~SPD+CV+RD+RDNORM+DIFFP,data=data.train)

# Make predictions (i.e., with probability threshold equal 0.5)
data.test$predicted.prob <\- predict(rf,data.test, type = "prob")
data.test$predicted.prob <\- data.test$predicted.prob[, "1"]
threshold <\- 0.5
data.test$predicted.response <\- ifelse(data.test$predicted.prob >= threshold,
1, 0)

# Assess accuracy
accuracy <\- mean(data.test$predicted.response==data.test$cartel)
accuracy

# Classifications in Part 3
data_part3 <\- read.csv("/path/to/my/directory/data_prep.csv", sep=";")
data_part3$predicted.prob <\- predict(rf,data_part3, type = "prob")
data_part3$predicted.prob <\- data_part3$predicted.prob[, "1"]
threshold <\- 0.5
data_part3$predicted.response <\- ifelse(data_part3$predicted.prob >=
threshold, "collude", "compete")

# Write csv for submission to lecturer
data_part3_final <\- data_part3 |>select(ID, predicted.response)
write.csv(data_part3_final, "/path/to/my/directory/data_part3.csv",
row.names=FALSE)