IEEE Computational Intelligence Magazine - May 2021 - 64

In this work, we propose a computational intelligence (CI) model, based on
evolutionary game theory [4], [5], to
study the VAT fraud dynamics of buyers
and sellers in an economic system. The
goal of the model is to represent a network of players-either cooperating (correctly declaring VAT) or defecting
(incorrectly declaring VAT)-linked by
their pairwise transactions. Evolutionary
game theory has been applied to models
of cooperation such as the well-known
prisoner's dilemma [6]-[8], snowdrift
games [9], [10], or trust dilemmas [11],
[12]. These game models represent one of
the most prominent CI techniques for
representing economic markets and
designing economic policies [13].
The application of -evolutionary game
models to study tax fraud and evasion is,
however, very limited [14]-[17], and nonexistent when focusing on consumption
taxes such as VAT.
Our CI model is studied in a structured population where players are
linked by means of a social network of
transactions. Here, players are given two
possible strategies: being a cooperator C
or being a defector D (i.e., a free rider).
The model considers the amount of tax
accrued on transactions not declared by
the free riders, a perceived probability of
being inspected by the tax agency, and
the corresponding fine when tax evasion
is detected. Cooperators, who are players
correctly paying their taxes, receive a
recognition or social reward; however,
they can also have their transactions
inspected, with a certain probability,
when their transaction records do not
match those of their transaction partners
in the network.
The combination of CI techniques
with agent-based modeling (ABM) [18],
[19] offers many opportunities for practitioners [20], and our work is a perfect
example. Our model represents players of
the tax system as agents on nodes of a
heterogeneous social network [21]. The
social network follows a power-law distribution, equivalent to the scale-free
network topology used in previous studies for promoting cooperation in social
dilemmas [22]. This social network is
weighted, with weights of the edges rep-

resenting values of the tax debt associated with the transactions between two
linked nodes. These weights make the
model a mixed game [23] where players
have different payoff matrices depending
on the volume of their transactions. The
players, through a social evolutionary
learning process, can imitate others' strategies by using an evolutionary update
rule and a mutation operator to randomly modify their own strategies.
We used real-world data from the
Canary Islands tax agency to feed most
of the parameters of the model and fit
the power-law distribution of the scalefree social network [24]. After investigating the general dynamics of the model
and effects of having well-mixed and
structured populations on scale-free
-networks with different properties, we
focused our experiments on determining policies to promote cooperation and
reduce the number of players who do
not correctly pay their consumption
taxes. To achieve this goal, we defined
different experimental scenarios that
allow us to understand when the best
cooperative behaviors occur. These scenarios include policies regarding the
shared pressure to increase the perceived
probability of being inspected for high
and low transactions and how diversity
in subjective probabilities affects the levels of cooperation in the population; the
impact of modifying the reputational
reward for cooperators; and a sensitivity
analysis on different inspection fines for
defectors or free riders.
In the next section (i.e., Section II),
we discuss related work and the motivation of our study. Details of the CI
agent-based model are then described in
Section III. Section IV presents the analysis of real data from the tax agency and
setup of the model. The results and
model's dynamics are discussed in Section V. Finally, Section VI summarizes the
key contributions.
II. Background and Related Work

The neoclassical economic model on tax
fraud by Allingham and Sandmo [25] is
considered one of the cornerstones of
the economic analysis of tax evasion.
They represent how individual agents

IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2021

decide to evade taxes, while also considering how the government would eventually punish them. However, this model
is unable to explain low levels of fraud
under low penalty and detection rates.
Bordignon [26] was one of the first to
describe this problem and the need to
explain tax fraud using explanation other
than just selfishness. Subsequent models
stress that tax compliance by agents is
dependent on how they perceive unfairness in their relations with not only the
administration, which is the vertical factor, but also the rest of the agents, which
is the horizontal factor [27].
When analyzing the horizontal factor,
the tax evasion literature tries to identify
how the compliance level of an agent
affects the compliance level observed by
the rest of the agents. Traxler [28]
attempted to model different levels of tax
evasion within and between groups of
agents. He was able to bring issues related
to belief management into the discussion,
extending the spectrum of policy instruments to the scope of changing individual beliefs, besides the economic
incentives. Prichard et al. [1] reflected on
the main reasons of the failure of mainstream neoclassical models in their survey.
They identified two main lines of
research that can address the limitations
of the traditional models by including the
relevance of behavioral aspects: experiments and ABM.
Experiments, as Alm [29] stated, are
not without problems, but they overcome the simplicity of theoretical models of individual choice, since they can
incorporate many explanatory factors
suggested by theory. They also favor the
combination of economic theory with
other disciplines like psychology,
increasing the realism of explanatory
factors of tax fraud [30].
Bonein [31] has identified different
levels of reciprocity between agents.
Under " strong reciprocity " , taxpayers
would tend to evade more (less) if they
observe a more (less) disadvantageous,
inequitable behavior by the remaining
agents. This completely contradicts the
predictions by self-interest models [32],
where agents are only motivated by
a future economic benefit. Frey and

IEEE Computational Intelligence Magazine - May 2021

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