An Agent-based Model Study on Subsidy Fraud in Technological
Transition
Hao Yang
1
, Xifeng Wu
1,
*
, Sijia Zhao
2
, Hatef Madani
3
, Jin Chen
4
and Yu Chen
1
1
SCS Lab, Department of Human and Engineered Environment, Graduate School of Frontier Sciences,
The University of Tokyo, Chiba 277-8563, Japan
2
Faculty of Economic and Management, East China Normal University, Shanghai 200062, China
3
Department of Energy Technology, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden
4
School of Economics and Management, Tsinghua University, Beijing 100084, China
*
Keywords: Agent-based Model, Technological Transition, Subsidy Fraud, Subsidy Policy, Socio Technical Transitions,
Complex System.
Abstract: The evolution of a society is inextricably linked to technological transition, which is based on both innovation
and dissemination of technologies. To protect the vulnerable new generation of technology, government
subsidies are one of the most common and effective tools. However, not all subsidy policies can lead to a
healthy development of market shares. Subsidy fraud is one of the most problematic issues that can arise
under an imperfect system. This paper identifies an interesting subsidy fraud like phenomenon via a validated
agent-based model. After analysing the mechanism of the transition of technology in the model, we drive the
condition upon which subsidy fraud could occur.
1 INTRODUCTION
Technological transitions are defined as a major
technological change in the way social functions
(e.g., transportation, communication, housing, food)
are achieved. For example, switching from
petroleum-fuelled cars to electrical vehicles, from
fossil-fuelled power stations to solar power stations
can both be regarded as technological transitions.
Innovation and dissemination of technology are very
important to the technological transition; hence the
promotion of innovation and the clarification of the
diffusion mechanism are the core goals pursued by
modern management science.
One of the most common and effective means of
helping the spread of new technologies is the use of
government subsidies. In particular, the government
provides subsidies through direct methods such as
price reductions or exemptions for companies or
consumers that use new technologies, or indirect
forms such as tax incentives. To a certain extent,
subsidies can compensate for the losses caused by the
immature new technology and stimulate companies
or consumers to use the new technology, thereby
*
Correspondence
helping to promote technological improvement and
increase the success rate of the realization of socio-
technological change.
However, in the actual implementation process of
government subsidies, many problems can arise. The
most met problem is subsidy fraud, which refers to
phenomena that individuals or firms provide incorrect
information when applying for government subsidies
or use subsidies in violation of the proposed intent
and agreement
1-2
. More specifically, there are
subsidies for different new energy sources in the low-
carbon transition process, while the government
promotes the diffusion of technologies through
advocacy (as in the case of the policy tools spreader
and subsidy introduced in Section 2.1.6 of the
methodology). Unfortunately, there is a gap between
actual policy effects and expectations, and when
social resources and policies are jointly focused on
specific things (e.g., low-carbon transition), it is
naturally very easy for the phenomena such as
subsidy fraud to arise under the influence of different
policy dissemination efforts (e.g., spreader) and
policy support efforts (e.g., subsidy). However, what
is the mechanism of subsidy fraud?
Yang, H., Wu, X., Zhao, S., Madani, H., Chen, J. and Chen, Y.
An Agent-based Model Study on Subsidy Fraud in Technological Transition.
DOI: 10.5220/0010887300003116
In Proceedings of the 14th International Conference on Agents and Artificial Intelligence (ICAART 2022) - Volume 1, pages 353-358
ISBN: 978-989-758-547-0; ISSN: 2184-433X
Copyright
c
 2022 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
353

Analysing the mechanism of subsidy fraud and
proposing solutions are particularly important to the
government's subsidy policy. This article tries to
analyse the mechanism of subsidy fraud through the
mathematical analysis of a validated agent-based
model.
3-10
2 MODEL
This work is based on a baseline model of A.Lopolito
11
. Main parameters are set as the same value in the
original study (refer to Appendix. Parameter setting).
2.1 Model Descriptions
The conceptual framework of the model is shown on
Fig 1. There are many firm agents and few spreader
agents (responsible for spreading the new
technology). Each firm agent’s behaviour is guided
by three mechanisms: expectation, networking, and
learning. They determine whether a firm agent should
convert to a supporter or a switcher to the new
technology, thus collectively determining the state of
technological transition. There are also two policy
tools: the subsidy policy controls the size of the
subsidy; and the lobbying policy controls the number
of spreader agents.
For the assumptions and mechanisms in the model
and the significance of each parameter, we drew from
the literature11.
Figure 1: Conceptual framework of the agent-based model
for technological transition.
2.1.1 Basic Assumption
As the basic assumption, the model assumes that there
are two technologies in the market, the new
technology and the old (traditional) technology. All
firms can freely choose one of the technologies to
produce goods in the next round. As the production is
completed, firms can further freely choose whether to
switch to a different technology or continue to use the
same technology.
The model consists of a finite number of firm
agents, 𝐼=1,2,⋯,𝑁

 ,𝑁

≪∞. It assumes that
all firms produce the same goods, and the market is
in the perfect competition state. Hence for all firms
that use traditional technology, their extra profit equal
to zero,
𝛱
 ,
=𝑅
 ,
−𝐶
 ,
=0 (1)
where 𝛱
 ,
, 𝑅
 ,
and 𝐶
 ,
represent the profit,
revenue and cost associated with the production at
time 𝑡 of firm 𝑖 which uses traditional technology.
As for firms using the new technology, risks and
profits coexist. These firms have an opportunity to
obtain extra profits, in the meantime, because the new
technology is often imperfect, they may suffer the
losses caused by unknown risks:
𝛱
 ,

=
𝑅

−𝐶
 ,


𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑝

0.5𝑅

−𝐶
 ,


𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 1 − 𝑝

(2)
where 𝑝 stands for the probability that the firm
will obtain the maximum profit by using the new
technology.
2.1.2 Expectation Mechanism
The basic structure of the expectation mechanism is
shown in Fig 2. Parameter 𝑒𝑥
 ,
represents the
expectation to the new technology of firm 𝑖 at time 𝑡,
which is affected by the following two ways:
(1) By the profit by using the new technology
𝑒𝑥
 ,
=𝑒𝑥
 ,
+𝛱
 ,

(3)
(2) By the encounter with a spreader of the new
technology
𝑒𝑥
 ,
=𝑒𝑥
 ,
+𝜂 (4)
Figure 2: Expectation mechanism affected by the profit
from the new technology or by the encounter with spreaders
of the new technology.
ICAART 2022 - 14th International Conference on Agents and Artificial Intelligence
354

2.1.3 Networking Mechanism
The basic structure of the networking mechanism is
shown in Fig 3. It mainly has the following two
functions.
Figure 3: Networking mechanism affected by the so-called
individual power and its sum over the whole network.
I. The formation of a user network of the new
technology
In our model, all the firm agents interact with each
other in a social space. We divide the distribution
space into several patches. Firms residing in the same
patch have closer social proximity. The formation
process of the network is shown in Fig 4.
(1) To establish a tie between firm 𝑖 and firm 𝑗 , the
following conditions need to be satisfied
1) Both firm 𝑖 and 𝑗 are supporters of the new
technology
2) The Social proximity between firm 𝑖 and 𝑗 is
less than the threshold value
(2) If a firm is no longer a supporter of the new
technology, all the ties from this firm will
disappear simultaneously.
Figure 4: The formation of a user network for the new
technology.
II. The reduction of cost for the new technology
We call all the shareable strategic resources
(except knowledge) individual power. The cost of a
firm agent using the new technology for production is
affected by two factors: the individual power (𝐼
,

)
of this firm, and the sum of individual power of all
firms in the network (𝑁


).
𝐶
 ,

=𝐶
 ,

−𝑐∙𝐼
,

−𝑛∙𝑁


(5)
where 𝑐 and 𝑛 are coefficients that adjust the
effectiveness of individual power of a firm and that of
the whole network. The individual power is further
affected by the profits:
𝐼
,

=𝐼
,

+𝛱
 ,
(6)
𝐸𝑛
,
=
𝐼
,

+𝐼
,

𝑖𝑓 𝑖 𝑎𝑛𝑑 𝑗 𝑎𝑟𝑒 𝑙𝑖𝑛𝑘𝑒𝑑
0 𝑖𝑓 𝑖 𝑎𝑛𝑑 𝑗 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑙𝑖𝑛𝑘𝑒𝑑
(7)
𝑁


=
∑
𝐸𝑛
,
 ,

(8)
2.1.4 Learning Mechanism
The basic structure of the learning mechanism is
shown in Fig 5, which is similar to the networking
mechanism.
When a firm uses new technology to produce, it
may succeed and obtain positive profits, or it may fail
and get losses. Learning mechanism affects the
failure rate through the knowledge owned by all the
firms in the network.
(1) Knowledge (𝐾
 ,
)
𝐾
 ,
=𝑟𝑎𝑛𝑑𝑜𝑚
𝐾
 ,
=𝐾
 ,
+𝜃𝐾
 ,
(9)
(2) Knowledge network structure
1) 𝐾𝑓
,
=
𝐾
 ,
+𝐾
 ,
𝑖𝑓 𝑖 𝑎𝑛𝑑 𝑗 𝑎𝑟𝑒 𝑙𝑖𝑛𝑘𝑒𝑑
0 𝑖𝑓 𝑖 𝑎𝑛𝑑 𝑗 𝑎𝑟𝑒 𝑛𝑜𝑡 𝑙𝑖𝑛𝑘𝑒𝑑
(10)
2) 𝑁𝐾𝑛

=
∑
𝐾𝑓
,
 ,

(11)
(3) The decay of new technology failure rate
𝑅𝑠𝑘

=𝑅𝑠𝑘

−𝜀∙𝑁𝐾𝑛

(12)
where 𝑁𝐾𝑛

represents the network knowledge at
time 𝑡, 𝑅𝑠𝑘

represents the failure rate of using new
technology to produce.
Figure 5: Learning mechanism.
An Agent-based Model Study on Subsidy Fraud in Technological Transition
355

2.1.5 Technological Transition
Firms become supporters of the new technology,
when 𝑒𝑥
 ,
exceeds a critical value. Firms that use the
new technology are called switchers. A firm can
become a switcher only if the expected profit of the
new technology is positive, 𝐸𝛱
 ,

>0. Details can
be found in the following items.
(1) Conditions for becoming a supporter (𝑒𝑥
 ,
)
𝑓𝑖𝑟𝑚 𝑖
𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡
→
𝑒𝑥
 ,
>0.75→ 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑒𝑟
𝑒𝑥
 ,
≤0.75→𝑛𝑜𝑡 𝑠𝑢𝑝𝑝𝑜𝑟𝑡𝑒𝑟
(13)
(2) Conditions for becoming a switcher (𝐸𝛱
 ,

)
𝑓𝑖𝑟𝑚 𝑖
𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡
→

𝐸𝛱
 ,

≤0→
𝑡𝑟𝑎𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙
𝑡𝑒𝑐ℎ𝑛𝑜𝑙𝑜𝑔𝑦
→
𝑛𝑜𝑡
𝑠𝑤𝑖𝑡𝑐ℎ𝑒𝑟
𝐸𝛱
 ,

>0→
𝑛𝑒𝑤
𝑡𝑒𝑐ℎ𝑛𝑜𝑙𝑜𝑔𝑦
→𝑠𝑤𝑖𝑡𝑐ℎ𝑒𝑟
(14)
where the expectation profit to the new
technology can be calculated by the flowing equation:
𝐸𝛱
 ,

=𝐸

𝑅


−𝐸𝐶
 ,


=𝑒𝑥
 ,
∙𝑅

−
1
𝑒𝑥
 ,
∙𝐶
 ,

(15)
2.1.6 Policy Tools
Two policy tools are considered in this model: the
subsidy policy and the lobbying policy.
(1) Subsidy Policy
This policy is realized by adjusting the size of the
subsidy to cause an impact on the market.
After introduced the subsidy policy, the profit for
each agent changes as follows:
𝛱
 ,

=𝛱
 ,

+𝑠𝑢𝑏𝑠𝑖𝑑𝑦 (16)
(2) Lobbying Policy
This policy mainly affects the market by adjusting the
number of spreader agents. Spreader agents do not
participate in the actual production of goods, on the
other hand, they are effective in the market through
the expectation mechanism. They will automatically
find firm agents that do not have high expectations for
the new technology. By lobbying these firm agents,
spreaders can increase firms’ expectations for the new
technology 𝑒𝑥
 ,
, hence promoting the spread of the
new technology.
(3) Lobbying Policy
This policy mainly affects the market by adjusting the
number of spreader agents. Spreader agents do not
participate in the actual production of goods, on the
other hand, they are effective in the market through
the expectation mechanism. They will automatically
find firm agents that do not have high expectations for
the new technology. By lobbying these firm agents,
spreaders can increase firms’ expectations for the new
technology 𝑒𝑥
 ,
, hence promoting the spread of the
new technology.
3 RESULTS
The model implementing is based on Netlogo
platform. A population of N = 100 firms located on a
grid sized 32×32，and the model includes spreader
agents randomly moving within the social space to
inform those firms that have not yet adopted the niche
technology.
The parameterisation used is summarised in Table
1.
3.1 The Critical Condition
In the case of 𝑆𝑢𝑏𝑠𝑖𝑑𝑦=0, we can derive:
𝐸𝛱
 ,

=𝑒𝑥
 ,
∙𝑅

−
1
𝑒𝑥
 ,
∙𝐶
 ,

>0 ⇔ 𝑒𝑥
 ,
>

𝐶
 ,

𝑅

(17)
Combined with the initial conditions 𝑅

=
1.5 ,𝐶
 ,

=1, we can deduce the condition for
firms to become switcher without the subsidy:
𝐸𝛱
 ,

>0 ⇔ 𝑒𝑥
 ,
>


.
≈0.816 (18)
Since the condition for firm 𝑖 to become a
supporter has been set as 𝑒𝑥
 ,
≥0.75, clearly the
prerequisite for becoming a switcher is “being a
supporter”, which is also an intuitively plausible
ICAART 2022 - 14th International Conference on Agents and Artificial Intelligence
356

scenario. If the firm does not support a technology, it
is almost impossible for it to use it.
However, due to the introduction of a subsidy, the
structure of Eq. (17) has been changed into the
following:
𝐸𝛱
 ,

=𝑒𝑥
 ,
∙𝑅

−
1
𝑒𝑥
 ,
∙𝐶
 ,

+𝑆𝑢𝑏𝑠𝑖𝑑𝑦>0
(19)
Hence a special case emerges: the condition to
become a switcher can be weaker than the condition
to become a supporter. From Eq. (19), we may
calculate that the critical size of the subsidy is 20.8%.
When 𝑆𝑢𝑏𝑠𝑖𝑑𝑦≤20.8%, the condition to become a
switcher is stronger than the condition to become a
supporter. In other words, the prerequisite for
becoming a switcher is to become a supporter. But
when 𝑆𝑢𝑏𝑠𝑖𝑑𝑦>20.8%, the situation will change,
and the prerequisite is no longer necessary. Because
the government subsidies are too strong, many firms
are willing to try to use new technology for
production even if they have not yet become
supporters of it. In such a scenario, many firms try out
the new technology, not because they are optimistic
about the technology, just because they are interested
in the large number of subsidies. Even though these
firms are willing to use niche technology for the
production activities, they do not make any efforts,
such as conducting the experiments or accessing the
supporter network, to develop the new technology.
3.2 Numerical Experiments
Even if the same parameter settings are used, the
model is still affected by random factors. To obtain
meaningful results, we average the outputs of 100
experiments, each of which contains 2600 timesteps
and is under the same initial conditions.
Through these numerical experiments, we found
that when the subsidy rate is higher than 20.8%, both
numbers of supporters and switchers quickly increase
to 100%. But if we cancel the subsidy, the entire
market reverses instantly. Although the number of
supporters can remain above 80%, the number of
switchers instantly becomes single digits, see the top
panel of Fig. 6. This result means that the entire
market is in an abnormally unhealthy state under the
too high subsidy: Firms use the new technology just
for the subsidies; when the subsidy is cancelled, those
firms who are not the real supporters of the new
technology leave the market instantly. Indeed, the
state after the cancellation of subsidy is consistent
with the stable state developed from the beginning
without the subsidy. This means that government
subsidies are completely ineffective. It is a
completely failed policy because the government has
spent huge amounts of money, but they did not reach
the goal of promoting the new technology.
Figure 6: Critical value experiment
(0 - 1500 timesteps: Subsidy = 21%, Spreader = 1.
1500 - 2600 timesteps: Subsidy = 0, Spreader = 1).
4 CONCLUSIONS
Government subsidies are an important factor to help
niche technology grow in the early stage of
technological development. By compensating for the
lack of profitability of technology, it can increase the
expected benefits of firms who have adopted the new
technologies and attract more firms to complete the
technological transition. However, due to regulatory
loopholes and other reasons, companies that only
hope to be decorated with the concept of new
technology or just want to defraud subsidies will
consume many social resources. Moreover, the fake
illusion of prosperity of the new technologies will
present an illusion to the industry and the
government. Once the sign of bubble collapse
emerges, these companies often get out fast causing
chaos in the corresponding industrial field. Therefore,
this article hopes to find the critical condition under
which firms may commit subsidy fraud.
Currently, we have obtained interesting
preliminary results and phenomena. At the same time,
as illustrated in the introduction section, we find that
An Agent-based Model Study on Subsidy Fraud in Technological Transition
357

subsidy fraud is prevalent in the low-carbon transition
process, which will help future validation studies of
the model. In addition, more rigorous and nuanced
studies, such as the assumptions adopted by the model,
need further refinement.
In the future, we also would like to further explore
how to systematically avoid the risk of subsidy fraud
and find a way to set up subsidy policies so that the
development of new technologies can be sustained
after the withdrawal of subsidies.
REFERENCES
Økokrim, Annual Report 2007, Norwegian national
authority for investigation and prosecution of economic
and environmental crime, Oslo, (2008).
Gottschalk, Petter. Categories of financial crime. Journal of
financial crime (2010).
Lopolito, Antonio, Piergiuseppe Morone, and Roberta
Sisto. Innovation niches and socio-technical transition:
A case study of bio-refinery production. Futures 43.1
(2011): 27-38.
Morone, Piergiuseppe, and Antonio Lopolito. Socio-
technical transition pathways and social networks: a
toolkit for empirical innovation studies. Economics
Bulletin 30.4 (2010): 2720-2731.
Lopolito, Antonio, Piergiuseppe Morone, and Richard
Taylor. An agent-based model approach to innovation
niche creation in socio-technical transition pathways.
Economics Bulletin 31.2 (2011): 1780-1792.
Victor, D., Geels, F. and Sharpe, S. Accelerating the low
carbon transition the case for stronger, more targeted
and coordinated international action. (2019). [online]
Available at: http://www.energy-transitions.org/
sites/default/files/Accelerating-The-
Transitions_Report.pdf [Accessed 21 Jan. 2020].
IPCC I. Working group III contribution to the fifth
assessment report of the intergovernmental panel on
climate change. (2014).
Geels F W. Technological transitions as evolutionary
reconfiguration processes: a multi-level perspective and
a case-study. Research policy, 2002, 31(8-9): 1257-
1274.
Wu X, Xu Y, Lou Y, et al. Low carbon transition in a
distributed energy system regulated by localized energy
markets. Energy policy, 122 (2018): 474-485.
Sun, Y. A study on crisis in an agent-based socio-economic
system. Doctor. Tokyo University. (2018).
Lopolito, Antonio, Piergiuseppe Morone, and Richard
Taylor. Emerging innovation niches: An agent-based
model. Research Policy 42.6-7 (2013): 1225-1238.
APPENDIX
Table 1: Parameter setting.
Type Denotation Valuation Type Denotation Valuation
𝐺𝑙𝑜𝑏𝑎𝑙
𝑁

100
𝐺𝑙𝑜𝑏𝑎𝑙
𝑝

0.5
𝑁

1
𝑅𝑠𝑘

1−𝑝

𝑁𝐸
0.75
𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙𝑃
0
𝜂
0.02
𝑅𝑎𝑑𝑖𝑢𝑠
1
√
𝜋
𝜋
0.001
𝐶𝑒𝑥

0.5
𝑛
0.01
𝐹𝑖𝑟𝑚 𝑖
𝑒𝑥

,

0.5
𝑐
0.01
𝐼

,


[0, 0.3]
𝜃
0.025
𝐾

,

[0, 0.01]
𝜐
2
𝐶𝑛

,

0.5
𝑆𝑢𝑏𝑠𝑖𝑑𝑦
0
𝐸𝛱

,



(15)
𝑅

1.5
𝛱
,
,𝛱

,


(1), (2)
𝑁


(8)
𝐿𝑖𝑛𝑘 𝑖,𝑗
𝐸𝑛
,
(7)
𝑁𝐾𝑛

(11)
𝐾𝑓
,

(10)
ICAART 2022 - 14th International Conference on Agents and Artificial Intelligence
358