Post on 28-Dec-2015
1
Game theoretical analysis of hospital expense claiming
strategy under global budgeting policy
Reporter： Juin-Yang Wang
Advisor ： Cheng-Han Wu
Date ： January 2013
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
2
Content
1
2
3
4
Introduction
Literature Review
The Model
Anticipated Contribution
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
3
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.
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
4
Motivation
ConcernGlobal budget and deduction system
Claim strategy and points
Decision behavior
Competition characteristics
Interactive scenerios
Hospital
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
5
Background
This research
Deduction System
Global Budget System
National Health Insurance
Expenditure cap
Game theory what condition ?
best response strategy Global Budget andDeduction System
Get points by the deduction
Points multiply point-value
Overallclaim points
Under global budget
Over global budget
Chi（ 2005） Global budget No trust mechanism Grow up Dilemma
Hung（ 2010） Fee for service Discount No decreasing the
growth of expenses
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
6
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
Objectives
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
7
Literature Review
1. the hospital produces the behavior of competition in claim points,
2. the hospital doesn't have the motive of cooperation
Hsu et al.（ 2007a）
Static equilibrium analysis
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
8
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
Hsu et al.（ 2007b）
Game theoretical model
Literature Review
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
9
Doctors will collaborate with each
other for more profits
Fan, Chen and Kan（ 1998）
Empirical economic method
Literature Review
Medical quality and medical
service quantity will drease
Mougeot and Naegelen（ 2005）
Welfare economics theorem
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
10
1. Treadmill effect
2. The effect serve quantity and point-value is anti-toward
Benstetter and Wambach（ 2006）develop expenditure price system
Literature Review
1. Doctor will strengthen of treatment
2. Admission quantity increase
3. Decrease of point-value
4. Prisoner's dilemma
Cheng et al. （ 2009）
Generalized estimating equation
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
11
Develop model
decision claim strategy
best response function
optimal solution
Nash equilibrium
The model
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
12
The model
1. Introduction
Global Budget System
Deduction System
Development the model
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
13
The model-deduction process
The hospitals who choose
under- budget strategy
The two heterogeneous hospitals ( , )i j
DeductionTwo hospitals
of no over budget
Over budget
No deduction
The hospitals who choose over-budget
strategy
Growing deduction
Commondeduction
value of point reveal
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
14
The model - notation
Decision
Variable
Parameter
the points of calim by the -th hospitals , 1,2 , i i j i j ;
Global Budge i iB b;
iq
Bv
T
1 c
i
ib points of target by the i-th hospitals , 1,2 , i j i j ;
point-value
claim upper limit of the tolerable /T B v ;
share for over-budgeting hospital
share for all hospital
unit cost from unit claiming points surplus for the -th hospital , 1,2 ,i i j i j ;
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
15
The model - notation
Global budget
overall claimn amount
claim upper limit
of the tolerate
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
16
( ) (1 )( ) ,
(1 )( ) , otherwise
i i ii i j i j i i i
i j i j
i
ii i j i
i j
q b qv q q q T q q T cq if q b
q q B q q
qv q q q T cq
q q
d.v.
the growing and under take amount
the commonand under take amount
No over-budget
Over-budget
can tolerate the excess amount of
claim
The model - notation
Surplus of i hospital
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
17
health market
Best response strategy
hospitalhospitali j
1Hospital i
chooses under-budget strategy
2Hospital j
chooses over-budget strategy
j jq b≦ j jq b
The model Best response strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
18
The model
hospital
Scenario 1Hospital j chooses under-budget strategy
i
under-budget over-budget
let
Best response strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
19
when
so
The model
Scenario 1Hospital j chooses under-budget strategy
Best response strategy
, exist
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
20
Scenario 2
The model
hospital
over-budgetunder-budget
i
let
Hospital j chooses over-budget strategy
Best response strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
21
, solvelet
when
so
if
The model Best response strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
22
Take for example
The model Best response strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
23
Scenario 2
let
when
so
if
The model Best response strategy
Hospital j chooses over-budget strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
24
The model Best response strategy
Take for example
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
25
let
when
so
if
The model Best response strategy
, solve
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
26
The model Best response strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
27
let
when
so
if
The model Best response strategy
, solve
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
28
Scenario 1
Scenario 2
if
The modelBest response strategy summary
Hospital j chooses over-budget strategy
Hospital j chooses under-budget strategy
existif
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
29
hospital 2hospital 1 over-budget
hospital 2hospital 1
onehospital
The model
over-budget
over-budget
Equilibrium strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
30
* * * *1 1 2 1 21π , π ,q q q q， *
1 1 1 22*
2π , π ,q b q b，
* *1 1 2 2 1 2 π , π ,b q b q， 1 1 2 2 1 2π , π ,b b b b，
1 1
(growing)
q b
2 2
no growing
q b
2 2 2 2(growing) (no growing )q b q b
hospital 2
hospital 1
Strategic game
The model Equilibrium strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
31
object function of hospital 1
object function of hospital 2
1 1 2 2,q b q b
The model Equilibrium strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
32
1 1 12 2
1 2 1 2
11 2
1 11 2 2
( 1 ) ( ) ( ) ((
)( )
( ) ( ))
T q B T b qT T B Tc v
q q q q B q qq
B q qq
22 1
2
1 2 12 2
1 2 1 2
( 1 ) ( ) ( )
( ) ( )( )
Tv q B T v B b qc
q qq
q B q q
1 1 2 2,q b q b
1 2
2 1
( ) 0
( ) 0
q
q
solution
The model Equilibrium strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
33
1 1 2 2,q b q b 1
1
2
2
0
0
q
q
solove
*1
12 ( ) ( )( ) 4 (2 )
8
Bc c Bc b
cq
*2
12 ( 2 ) ( )( 2 ) 4 (2 )
8
Bc c Bq
c b
c
2 2
( 1 ),
( ) ,
( 2 ) 2(2 )
Tv
B T v
Bc Bc
The model Equilibrium strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
34
1 1 2 2,q b q b
1 1 11 1 2 1 2 1
1 2 11
2
( )( ( ) (1 )( ) )
( ) ( )
q b qv q q q T q q T cq
q q B q q
22 21 2
22
1
( (1 )( ) )( )
qv q q q T cq
q q
2 2 1 22 2
1 2 1 2
12
1 2
1
1
2
2
( 1 ) ( )( )( ) ( )
( 1 )
( )
q q v B b qc B
q q B q q
B qc v
q
qq q
Solution
The model Equilibrium strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
35
1 1 2 2,q b q b
2 1 23 3
1 2
212
1 21
( 1 ) ( 1 ) ( )2 ( ) 0
( ) ( )
q v B b qB
q q B q qq
212* ( 1 )B q
qc
qc
*2 2q b
2 2q b
The model Equilibrium strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
36
1 1 2 2,q b q b
1 1 1vq cq
2 2 2vq cq
1*
1 bq
2*
2 bq
The model Equilibrium strategy
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
37
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
National Yunlin University of Science & Technology Department of Industrial Engineering and Management Supply Chain Management Laboratory
Game Theory
38
The model – Expectation result
reseach schedule
work item 2012年 2013年7 8 9 10 11 12 1 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
Future research
39