IEEE Computational Intelligence Magazine - May 2021 - 72

α = 0.2, probdH = 0.02

0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1

Θ′H

1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

Θ′L
α = 0.4, probdH = 0.02

1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1

Θ′H

C. Balancing between the Subjective
Audit Probability for High and Low
Transactions

Θ′L
α = 0.4, probdH = 0.5

0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1

Θ′H

1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

Θ′L
0

0.2
0.4
0.6
0.8
Final Frequency of Cooperators

FIGURE 9 The upper and middle heatmaps show sensitivity analysis on HlL and HlH for
a = 0.2 and a = 0.4 (real data scenario where prob dH = 0.02). The bottom heatmap shows
the sensitivity analysis when prob dH is 0.5 and a = 0.4 for comparison. We observe that
increasing the inspection probability for low transactions is preferable in the real world scenario where prob dH = 0.02, but this conclusion does not apply when we have the same number
of low and high transactions in the network (see the lower heatmap).

as the most prevalent games for the
parameter values.
The lower plot of Figure 8 shows the
dynamics of the model with the above
assortative and disassortative topologies and a well-mixed population. As
observed with low density networks,
disassortativity favors cooperation when
the game is hard (high values of a).
Assortativity plays its role in promoting
cooperation when the game is easy. We
see from Table III that the real network
has high diameter values and the clustering coefficient is 0. Therefore, the
dynamics of the game with this network
is equivalent to neither full assortative nor full disassortative networks
(Table III). Instead, the low density and
large diameter of the real network
explain the slow decay of cooperation
for large a values.

IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2021

One of the main insights the analysis of
real data from the Canarian tax agency
revealed was the distinction between
two types of transaction volumes: high
and low. We would like to find the best
policy to promote cooperation and correct tax paying behavior by determining
the type of transaction the tax agency
must focus on. In order to understand
the impact of investigating these types of
transactions, we use the evolutionary
model to balance the focus on the subjective audit probability-which can be
modulated differently depending on the
transaction volume. Thus, we set different values for HlH and HlL, which
changes the construction of the probability linear function. We started from
base values of HlH = 0.5 and HlL = 0.5
and considered a wide range of pairs for
analysis, from 0 to 1 for both parameters.
Figure 9 has three heatmaps showing
the final frequency of cooperators for
different subjective audit probabilities.
The upper and middle plots show the
results when a is equal to 0.2 and 0.4,
respectively. The lower plot shows the
dynamics when the numbers of high
and low transactions are equal (i.e.,
prob dH is 0.5) and a = 0.4.

IEEE Computational Intelligence Magazine - May 2021

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