Game theoretical analysis of hospital expense claiming strategy under global budgeting policy Reporter ： Juin-Yang Wang Advisor ： Cheng-Han Wu Date ： January

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


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.


Game Theory

4

Motivation

ConcernGlobal budget and deduction system

Claim strategy and points

Decision behavior

Competition characteristics

Interactive scenerios

Hospital


Game Theory

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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


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


Game Theory

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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


Game Theory

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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


Game Theory

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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


Game Theory

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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


Game Theory

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Develop model

decision claim strategy

best response function

optimal solution

Nash equilibrium

The model


Game Theory

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The model

1. Introduction

Global Budget System

Deduction System

Development the model


Game Theory

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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


Game Theory

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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 ;


Game Theory

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Global budget

overall claimn amount

claim upper limit

of the tolerate


Game Theory

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( ) (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


Surplus of i hospital


Game Theory

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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


Game Theory

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The model

hospital

Scenario 1Hospital j chooses under-budget strategy

i

under-budget over-budget

let



Game Theory

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when

so

The model

Scenario 1Hospital j chooses under-budget strategy


, exist


Game Theory

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Scenario 2

The model

hospital

over-budgetunder-budget

i

let

Hospital j chooses over-budget strategy



Game Theory

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, solvelet

when

so

if



Game Theory

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Take for example



Game Theory

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Scenario 2

let

when

so

if




Game Theory

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Take for example


Game Theory

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let

when

so

if


, solve


Game Theory

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Game Theory

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let

when

so

if


, solve


Game Theory

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Scenario 1

Scenario 2

if

The modelBest response strategy summary


Hospital j chooses under-budget strategy

existif


Game Theory

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hospital 2hospital 1 over-budget

hospital 2hospital 1

onehospital

The model

over-budget

over-budget

Equilibrium strategy


Game Theory

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* * * *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


Game Theory

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object function of hospital 1

object function of hospital 2

1 1 2 2,q b q b



Game Theory

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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



Game Theory

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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



Game Theory

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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



Game Theory

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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



Game Theory

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1 1 2 2,q b q b

1 1 1vq cq

2 2 2vq cq

1*

1 bq

2*

2 bq



Game Theory

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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


Game Theory

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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

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Documents

Game theoretical analysis of hospital expense claiming strategy under global budgeting policy Reporter ： Juin-Yang Wang Advisor ： Cheng-Han Wu Date ： January