Эффективность работы вуза на рынке выпускников в условиях

Gladkova Margarita
Graduate School of Management
St. Petersburg State University, Russia
E-mail: rita.gladkova@gmail.com
Supervisor: Nikolay A.Zenkevich
GAME-THEORETICAL MODEL
“QUALITY-PRICE” UNDER
COMPETITION ON THE INDUSTRY
MARKET
December, 2007
Model assumptions
• Customer: i  N , N  {1,2}; s2  s1
   ,       1,  0
s  p,
U  ( p, s )  
 0,
p  s
p  s
• Decision-making process:
si
si
 
si  s0 , si  s, si , pi  0
pi
Company’s profit function
 i  pi , p j , si , s j , si , s j   pi Di  pi , p j , si , s j   csi   F si ; i, j  1,2
pi , Di ( pi , p j , si , s j ), c( si ), F ( si )
si  s0 , si  s, si , pi  0
Cost functions:
2
1. c( si )  ksi , k  0
2
2. F ( si )  bsi  s0  , b  0
Covered market:
D1 ( p1 , p 2 , s1 , s 2 ) 
p 2  p1

s 2  s1
p 2  p1
D2 ( p1 , p 2 , s1 , s 2 )   
s 2  s1
Uncovered market:
D1 ( p1 , p 2 , s1 , s 2 ) 
p 2  p1 p1

s 2  s1 s1
p 2  p1
D2 ( p1 , p 2 , s1 , s 2 )   
s 2  s1
Covered market. Solution
If
(2   ) 2
 [ s, s 0 ]
18k
 s1 *  s0
 *
 s 2  s0
 *   2   2   2


 s 
 p1 

3  18k



2
 p *  2     2     s 
 18k

 2
3



s1*  s


2
 * (2   )
s2  18k
 *   2 
 D1 
3

 D2*  2   

3
 *   2 2  (2   ) 2

2



s

k
s


 1
9
 18k


4

2    (2   ) 2

*
2 

s

324k
9
Covered Market
Parameters
(2   )
 [ s, s 0 ]
18k
Quality ranges
Firm 1
Firm 2
2
s
s
s
(2   ) 2
 s0
18k
0
s
0
Differentiation level
s, s 
s2*  s
s, s 
s0  s
s, s 
s2  s
*
2
s
0
NE quality
levels
0
0
0
s
*
2
*
2
*
Uncovered Market
Parameters

0.0241
0.1266
k
0.1266
k

0.1266
0.1266
2
k


 s , s0
 s,




 s, s0
 s , s0 ,
Firm 1
s
0
Firm 2
s
s
s
s
0
0
s2
 s,
s
s
 s0
s
s2
0
0
*
0
2
k
s , s 
s2*  s1*
s
s2**  s1**
**
1
0
s
0
Differentiation level
*
2
0
s
0
NE quality
levels
*
1
 s0
2
k


2
k

0.0241
2
k


 s , s0 ,
2
k

0.0241
2


0.0241
2
Quality ranges
**
s
***
1
, s2**

***
2
,s

s2***  s1***
s, s 
s0  s
s, s 
s2  s
0
**
2
**