Information Technology Reference
In-Depth Information
1
a)
100% a-types
c)
100% c-types
0.8
0.001
0.6
fixed penalty: h=5
fixed penalty: h=10
backaudit: 5 periods, h=4
0.4
0.2
0
0
50
100
150
200
0
50
100
150
200
0.5
d)
b)
100% d-types
100% b-types
0.06
0.4
0.04
0.3
0.2
0.02
0.1
0
0
0
50
100
150
200
0
50
100
150
200
time step
time step
Fig. 1.
Time evolution for the participation in black market services for a society consisting of
100% a-type (panel a), 100% b-type (panel b), 100% c-type (panel c), and 100% d-type (panel
d) agents. Results are reported for different enforcement mechanisms: fixed compliance period
h
= 5 (solid, black),
h
= 10 (dashed, red), and backaudit (dashed-dotted, blue). Audit probability
is
p
a
= 10% in each case.
Before analyzing the heterogeneous agent model it is instructive to consider first the
case of a black market with all agents being of the same type. The resulting percentage
of black market share as a function of time is shown in Fig. 1 where we also compare
the different enforcement schemes.
The first case of endogenous non-compliant selfish agents is shown in Fig. 1a. At
time step zero we correspondingly set the share of black market participation to
p
bm
= 1.
Due to the enforcement mechanisms the black market share is significantly reduced
because at each time step a certain percentage of the remaining non-compliant agents
are forced to become compliant. Before reaching a stationary value small oscillations
are observed since after
h
time steps the first detected agents can become non-compliant
again. Notably, the black market share is reduced strongest for the backaudit mechanism
Fig. 1b reports the result for copying b-type agents. As initial condition all agents are
set to 'compliant'. Since b-types tend to copy the behavior of their social network only
few of them change their behavior and the equilibrium value for the black market share
for all enforcement mechanisms approaches a rather small value between 4% and 5%.
It should be noted that the equilibrium value is independent of the initial condition. If
we would have set all agents to non-compliant at time step zero, the audits would have
reduced the black market share to the same equilibrium value than shown in Fig. 1.
