Game theoretical analysis of
hospital expense claiming
strategy under global
budgeting policy
Reporter：Juin-Yang Wang
Advisor ：Cheng-Han Wu
Date ：January 2013
1
Content
1
Introduction
2
Literature Review
3
The Model
4
Anticipated Contribution
National Yunlin University of Science & Technology Department of Industrial Engineering and Management
Supply Chain Management Laboratory
2
Motivation
 Over budget is not always the best response
strategy
 The behavior of each hospital will be under
the influence of other hospitals
Dilemma
Therefore, the claim decision of
hospital is important.
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Supply Chain Management Laboratory
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Motivation
Concern
Global budget and deduction system
Claim strategy and points
Decision behavior
Interactive scenerios
Competition characteristics
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Supply Chain Management Laboratory
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Background
Chi（2005）
Overall
Global
budget
claim points
No trust mechanism
This research
up
Game Grow
theory
Over global budget
Dilemma
Expenditure
cap
what condition ?
Hung（2010）
Under global
response strategy
GlobalDeduction
Budgetbest
and System
Fee for service
Discount
No decreasing the
Global Budget
growth ofSystem
expenses
Deduction System
budget
Get points by the
deduction
National Health Insurance
Points multiply pointvalue
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Supply Chain Management Laboratory
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Objectives
 Develop medel
 Consider other medical organization, derive best response
strategy
 Consider other medical organization, derive equilibrium
strategy
 Find out the condition of choosing over budget strategy
 Provide insights
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Literature Review
Hsu et al.（2007a）
Static equilibrium analysis
1. the hospital produces the
behavior of competition in claim
points,
2. the hospital doesn't have the
motive of cooperation
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Literature Review
Hsu et al.（2007b）
Game theoretical model
1. Low service quantities may
become the sub-game perfect
Nash equilibrium under infinite
repeated game
2. Improper design of GB system ,
moral hazard and risk
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Literature Review
Fan, Chen and Kan（1998）
Empirical economic method
Doctors will collaborate with each
other for more profits
Mougeot and Naegelen（2005）
Welfare economics theorem
Medical quality and medical
service quantity will drease
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Supply Chain Management Laboratory
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Literature Review
Benstetter and Wambach（2006）
develop expenditure price system
1. Treadmill effect
2. The effect serve quantity and
point-value is anti-toward
Cheng et al. （2009）
Generalized estimating equation
1. Doctor will strengthen of treatment
2. Admission quantity increase
3. Decrease of point-value
4. Prisoner's dilemma
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Supply Chain Management Laboratory
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The model
Develop
model
decision
claim strategy
best response
function
optimal
solution
Nash equilibrium
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Supply Chain Management Laboratory
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The model
1. Introduction
Global Budget System
Development
the model
Deduction System
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The model-deduction process
The two heterogeneous
hospitals (i, j)
Over
budget
Two hospitals
of no over
budget
Deduction
The hospitals
who choose
under- budget
strategy
The hospitals
who choose
over-budget
strategy
No deduction
Growing
deduction
Common
deduction
value of
point reveal
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The model - notation
Decision
Variable
qi
the points of calim by the i-th hospitals; i, j  1, 2 , i  j
Parameter
bi
points of target by the i-th hospitals ; i, j  1, 2 , i  j
B
v
Global Budge ; B  i bi
T
claim upper limit of the tolerable ; T  B / v

share for over-budgeting hospital
share for all hospital
1
c
i
point-value
unit cost from unit claiming points
surplus for the i -th hospital; i, j  1, 2 , i  j
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The model - notation
overall claimn amount
claim upper limit
of the tolerate
Global budget
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The model - notation
Surplus of i hospital
d.v.
the growing
and under take
amount
the common
and under
take amount
 
qi  bi
qi
v
q


(
q

q

T
)

(1


)(
q

q

T
)
  i
i
j
i
j
qi  q j  B
qi  q j
 
i  
qi 
 
v  qi (1   )(qi  q j  T ) q  q   cqi
i
j 
 

  cqi , if qi  bi

, otherwise
Over-budget
No
over-budget
can tolerate the excess
amount of claim
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The model
Best response strategy
health market
Best
response
strategy
hospital
hospital
i
j
1
Hospital i
chooses under-budget
strategy
q j≦ b j
2
Hospital j
chooses over-budget
strategy
q j  bj
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The model
Scenario 1
Best response strategy
Hospital j chooses
under-budget strategy
let
hospital
i
under-budget
over-budget
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The model
Scenario 1
when
Best response strategy
Hospital j chooses
under-budget strategy
, exist
so
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The model
Scenario 2
Best response strategy
Hospital j chooses
over-budget strategy
let
hospital
i
under-budget
over-budget
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The model
let
Best response strategy
, solve
when
if
so
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The model
Best response strategy
Take for example
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The model
Scenario 2
Best response strategy
Hospital j chooses
over-budget strategy
let
when
if
so
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The model
Best response strategy
Take for example
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The model
let
Best response strategy
, solve
when
if
so
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The model
Best response strategy
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The model
let
Best response strategy
, solve
when
if
so
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The model
Best response strategy summary
Scenario 1
Hospital j chooses
under-budget strategy
exist
if
Scenario 2
Hospital j chooses
over-budget strategy
if
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The model
Equilibrium strategy
hospital 1
hospital 2
over-budget
one
hospital
over-budget
hospital 1
hospital 2
over-budget
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The model
Equilibrium strategy
hospital 2
q2  b2 (growing)
q1  b1
hospital 1
(growing)
q2  b2
no growing
π1  q1* , q2* ，π1  q1* , q2* 
q2  b2 (no growing)
π1  q1* , b2 ，π 2  q1* , b2 
π1  b1 , q2* ，π 2  b1 , q2*  π1  b1 , b2 ，π 2  b1 , b2 
Strategic game
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The model
Equilibrium strategy
q1  b1 , q2  b2
object function of
hospital 1
object function of
hospital 2
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The model
Equilibrium strategy
q1  b1 , q2  b2
 1
T (1   )q1 T  T  ( B  T ) ( b1  q1 ) ( B  T )
 (q2 ) 
 c  v (



)
q1
(q1  q2 ) 2
q1  q2
( B  q1  q2 ) 2
 B  q1  q2

1
 2
Tv(1   )q1 ( B  T )v ( B  b2  q1 )
 (q1 ) 
 c 

2
q2
(q1  q2 )
( B  q1  q2 ) 2

2
solution
 1 ( q2 )  0
 
 2 ( q1 )  0
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The model
Equilibrium strategy
q1  b1 , q2  b2
solove
  1
 q  0
 1
 
  2  0
 q2
2 Bc(    )  (    )(      )  4c(2 Bc       )b1
8c
2 Bc(   2   )  (      )(   2   )  4c(2 Bc       )b1
q2 *  
8c
q1* 
  Tv(1   ),
  ( B  T )v ,
  (2 Bc   ) 2  2(2 Bc   )   2
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The model
Equilibrium strategy
q1  b1 , q2  b2
1  v(q1   (q1  q2  T )
(q1  b1 )
q1
 (1   )(q1  q2  T )
)  cq1
(q1  q2  B)
(q1  q2 )
 2  v(q2  (1   )(q1  q2  T )
q2
)  cq2
(q1  q2 )
  1
q2   q2 (1  v) ( B  b1  q2 )


c

B
(

)
 q
2
2
(q1  q2 )
( B  q1  q2 )
Solution  1

  2  c  v  B(1   )q1
 q2
(q1  q2 ) 2
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The model
Equilibrium strategy
q1  b1 , q2  b2
q2  b2
 2 1
(1   ) q2 (1  v) ( B  b1  q2 )

2
B
(

)0
2
3
3
q1
(q1  q2 )
( B  q1  q2 )
q2*  b2
*
1
q
 Bc(1   )q2
 q2 
c
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The model
Equilibrium strategy
q1  b1 , q2  b2
 1  vq1  cq1
q1*  b1
 2  vq2  cq2
q2*  b2
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Anticipated Contribution
 We attained the equilibrium strategy
 The factor influence claim behavior by empirical and
parameter analysis
 Discuss the current allocation of medical resources
 Whether the hospitals be has speculate at behavior for
more profit
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The model –
Expectation result
Future research
reseach schedule
work item
7
2012年
8 9 10 11 12 1
2013年
2 3 4 5
6
Literature Review
and confirm topic
Develop the model
identification of
model rationality
Best response and
equilibrium strategy
Empirical and
parametric analysis
Conclusion and
insight
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