IEEE Computational Intelligence Magazine - May 2021 - 75

with high fines is the most convenient
option for promoting cooperation. In
the first scenario, rewarding cooperators
is almost invar iant for the model
dynamics. Therefore, both reward and
punishment strategies must be carried
out together while balancing the focus
on either high or low transactions or, at
least, apply them depending on the current scenario.
VI. Final Discussion

We presented the first evolutionary
game model for consumption taxes. This
model represents cooperators and defectors and includes parameters to penalize
tax evaders. It also considers the subjective probability of being inspected by
the tax agency, which can be modulated
with the size of the economic transaction. Players are linked through a
scale-free network. Both the network
topology and most of the model's
parameters are fed with real data from
the Canarian tax agency.
The stability and robustness of the
model were demonstrated by simulating
the effects of the undeclared quantity (a
parameter), initial distribution of the
population, and convergence to a steady
state. After illustrating the main dynamics, we evaluated the two main questions
for the tax agencies. First, we explored
whether the agencies must focus on
high or low transactions. We found that
it is better to increase pressure on low
transactions rather than high transactions. This is mainly due to the larger
number of low transactions in the network. But the level of this pressure on
low transactions is irrelevant once it is
higher than the pressure on high transactions. This result is in line with previous findings [36] which support policies
to increase audit probability but extend
them by differentiating the audit probability according to the transaction size.
Our results could encourage tax agencies to apply appropriate media actions
targeting small transactions rather than
high transactions.
Second, our analysis showed that
policies for either rewarding cooperators or punishing defectors must be
executed in conjunction with policies

The role of the inspection cost is significant only when
the game has an intermediate level of difficulty ... This
means that relying on the inspection cost to promote tax
compliance is more worthy when the population has a
mixture of cooperators and defectors.
for high and low transactions. For
instance, we observed that, when the
perceived inspection probability is
more significant for high transactions,
rewarding cooperators is more beneficial than increasing fines for defectors. This effect was consistent for
different difficulty levels of the game
(def ined through the a parameter).
However, when pressure is more
important for low transactions, punishing defectors prevails as the best
strategy. Our findings recommend tax
agencies to follow a constructive
approach to better reward companies
behaving well by publicizing reward
actions. These policies must be run in
conjunction with other measures (e.g.,
balancing pressure on either low or
high-value transactions).
The presented study has some limitations. The rewarding versus punishing
policies do not take into account possible costs. A method of evaluating these
two options by considering the costs
for the agencies could be valuable.
Researchers can also evaluate the
response of temporal changes in the network topology. For example, one can
study how temporal changes on the
type of transaction between players (i.e.,
d ij) can influence the game output as the
employed payoff matrix would also
change over time. A more comprehensive study about diversity in the subjective inspection probabilities of the
individuals can be performed as well.
Finally, a CI algorithm could identify
the most influential companies (nodes)
to be targeted with specific policies such
as in Robles et al. [62].
Acknowledgments

This work is jointly supported by the
Spanish Ministry of Science, Andalusian
Government, and ERDF under grants

EXASOCO (PGC2018-101216-BI00), SIMARK (P18-TP-4475) and
RYC-2016-19800. The data used here is
based on the project " Elaboration of a
Computable General Equilibr ium
Model for the Analysis of Fiscal Policies
on Sales Taxes " commissioned by the
Economy and Finance Council of the
Regional Government of the Canary
Islands (FULP, CN45/08 240/57/100).
We thank the Council of Economy,
Knowledge and Employment of the
Regional Government of the Canary
Islands for allowing us to use the results
of the latter project.
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