Information Technology Reference
In-Depth Information
0.4
30
a
b
c
d
c) Compliance period
0.35
a) Total black market share
25
0.3
20
0.25
15
0.2
10
0.15
5
0.1
0
0
100
200
0
100
200
0.5
0.5
0.2
0.4
a
b
0.4
b) Black market
share of agents
0.3
a
b
c
d
0.3
0.2
0.2
0.15
0.1
0.1
0
0
0
816
24
0
816
24
0.1
1
0.4
0.8
c
d
0.3
0.6
0.05
0.2
0.4
0.1
0.2
0
0
0
0
100
200
0816
24
0816
24
time step
Fig. 3.
The same as Fig. 2 but for a society consisting of 15% a-type, 65% b-type, 5% c-type, and
15% d-type agents
Fig. 2. Naturally most a-types are penalized with the maximum compliance period of
k
= 6
4 = 24 time steps. Only those which have been convicted also in previous time
steps (and therefore have to stay compliant) are penalized with a reduced compliance
period. On the other hand, the (few) convicted c-type agents are penalized with a com-
pliance period of
k
= 4 since their probability of repeatedly being non-compliant within
the backaudit period is vanishingly small.
Fig. 3 shows the analogous results for the parameter set 'G' derived for Germany and
also 15% of a-type agents. The reduced percentage of (compliant) c-types as compared
to France is compensated by the increased number of b-type agents which enhance
the black market participation as becomes apparent from Fig. 3a. In fact, the largest
contribution is now from the b-types (cf. Fig. 3b) in contrast the previous parameter set.
Note especially that the percentage of convicted b-types with a compliance period of 4
time steps is reduced from
∗
40% in Fig. 3 due to the concomitant
reduction of c-types which define the social norm of adjacent b-type agents.
We are now in the position to evaluate the black market share as a function of a-
type agents for the two parameter sets 'F' and 'G' derived above. Fig. 4 reports the
corresponding results for different audit schemes, i.e. fixed compliance period with
h
= 5
,
10 and backauditing with backwards auditing period of
b
p
= 5 and scaling factor
h
= 4 (cf. above). Within all auditing schemes we find a larger black market share for
the parameter set as deduced for Germany due to the smaller (larger) percentage of
c-(b-) type agents. The horizontal lines in Fig. 4 indicate the size of the shadow
∼
45% in Fig. 2 to
∼
