Financial Regulation:
A Game Theory Approach
Jiye Hu
China University of Political Science and Law
At the Law Faculty, University of Oxford
1 February 2011
Outline



Why Game Theory?
A Mixed Strategy Model
Application Legislation
Why Game Theory?
The formulation of Nash equilibrium has
had a fundamental and pervasive impact
on economics and social sciences, which
is comparable to that of discovery of the
DNA double helix in the biological
sciences.
Roger B. Myerson (2007 Nobel Prize laureate),
“Nash Equilibrium and the History of Economic Theory”,
Journal of Economic Literature 37，1067-1082, 1999.
Why Game Theory?
Game theory's method is to simplify a
situation by describing it in terms of players,
actions, payoffs, after which the players'
strategic interactions can be described.
Whether used explicitly or implicitly, this is a
highly useful approach to law.
Two Books:
Game Theory and the Law
Baird et al., Harvard University Press , 1994.
Game Theory and the Law
Rasmusen, Eric, Cheltenham, UK, 2007.
A Mixed Strategy Model
Who is regulator ?
European Banking
Authority
European Securities
and Markets Authority
European Insurance
and Occupational
Pensions Authority
Who is regulatee ?
Commercial Banks
Security companies
Insurance companies,
pension funds ……
A Mixed Strategy Model
Two strategies for both side:
two options can be selected by the regulator (G):
audit or not
two options can be selected by the regulatee (P) :
false claim or not
Assume they are both rational economic men
goals of regulator are detect false claimers and
punishment
goals of regulatee are to maximize their utility, by
falsely claim as much as possible under the condition of
weak supervision

A Mixed Strategy Model
REGULATEE (P)
R
E
G
U
L
A
T
O
R
(G)
False claim (γ)
True claim(1-γ)
Audit
(θ)
B-C,
-F
-C,
0
Non-audit
(1-θ)
-R,
E
0,
0
A Mixed Strategy Model
Assuming the regulatee’s probability of false claim is γ,
regulator’ expected benefits with auditing (in the upper line)
or not (in the under line) are, respectively:

In the upper line:
 G(1,  )  ( B - C )  (-C )(1-  )   B - C
In the under line:
 G(0,  )  - R  0(1-  )  - R
A Mixed Strategy Model
According to the basic assumption that regulatee
does everything to escape audition, γ* maybe the
optimum probability of offence. Then the regulator’
expected benefits are the same no matter how he
audits or not. Let Upper line=Under line, can
calculate the optimum probability of γ *：

* 
C
B R
We can drawing the result below; if we change cost C to
C’, we can get another γ ‘*:
Y: Regulator’s pay-off
F’
F
C
0
B+R-C
γ*
C’
C
X: Regulatee’s false probability
1
A Mixed Strategy Model

Similarly, we can calculate the regulator’s optimum audit
probability. Given probability of audition θ, regulatee’s
expected benefits with offending (in the left column) or not
(in the right column) are, respectively:
In the left column :
 G( ,1)  (- F )  E(1-  )  E -  ( E  F )
In the right column :
 G( ,0)  0  0(1-  )  0
A Mixed Strategy Model
According to the basic assumption that regulator
do his best to catch offence, θ* is the optimum
probability of audit. Then the regulatee’s expected
pay-off is the same no matter how regulator audits
or not. Let left column = left column, can calculate
the optimum probability of θ *：

*

E
EF
We can drawing the result below; if we change cost F to
F’, we can get another θ ‘*:
E
Y: Regulatee’s pay-off
θ*
1
0
E
F
X: Regulator’s audit probability
F
F’
A Mixed Strategy Model
It means, the regulator audits in the probability of θ
*, regulatee offends by the probability of γ* ,
accordingly.
 Here, regulatee’s offence probability depends not on
himself, but on the regulator: the lower execution cost
C for regulator, and the more bonus B and reputation R,
the more difficult for regulatee to commit.
 Similarly, the audit probability of regulator mainly
depends on regulatee’s expected benefit E and
punishment F, rather than on his own characteristic
-------Regulation dilemma

Application to Legislation
What could we learn from the model?
For the regulatee, if the regulator has a lower execution
cost C, whilst more bonus B and reputation R, he will be
less false claim. Here is a good example: Hong Kong’s
Independent Commission Against Corruption. ICAC’s R is
very large, so there is less false claim and corruption in HK.
 Obviously, when E >F, regulatee chooses to violate law
because punishment is insignificant even probably being
detected. Only if legal power F is much stronger than
offensive profits E, does regulatee choose to obey the law,
therefore the stronger legal power F is, the lower probability
offences happen and audition taken

Application to Legislation
What could we learn from the model?
 For the regulator, if the regulatee faces a lower
extra income E, whilst less fine F, he will be
induced to perform less audit. It means the
regulator are lazy to do their work because they
believe the regulatee will not “worth” to false claim.
 Obviously, when B and R are large enough,
regulator will be encouraged to audit.
Application to Legislation
So in Legislation, we can:
 Enlarge R, B, F for both encourage the regulator
and threaten the regulatee;
 In a real world, B, F can only be increased to a
certain extent, and reputation R can be relied on to
fill the gaps
 The education of regulators is necessary, and
they must have well qualified in good education
history, current working sense of honour, and
bright Prospects for the future.
Application to Legislation
So in Legislation, we can:
Reduce the extra income E, lessen the seduce for the
regulatee. This will be a little difficult in legislation; more
useful in law enforcement
 Reduce the regulation cost C, to let the regulatee accept
lower probability in false claim. “Centrelink” of Australia
mainly uses off-site audition, their cost will be lower then
other countries.

-
China Regulation Law over Banking Article 23: The banking
regulatory authority shall conduct off-site supervision of the business
operations and risk profile of the financial institutions of the banking
industry……
Application to Legislation
As market failures, the financial factor need to be
regulated;
 Based on the regulation theories, we can
construct a mixed strategy game theory model, to
simplify and describe the relationship between
regulator and regulatee.
 From the model, we know that regulator’s
reputation and bonus larger is better, whilst their
regulation cost lower is better

Application to Legislation
In the mean time, enlarge the regulatee’s
false punishment and reduce its expect of
false claim, will benefit the regulation effect.
 The regulation cost of regulator is a
extremely important element, it not only
related the cost-benefit analysis for the
regulator himself, but also impact the
regulatee’s false probability

Thank you!
jiyeh@cupl.edu.cn