Course outline I



Introduction
Game theory
Price setting
monopoly
– oligopoly
–

Quantity setting
monopoly
– oligopoly
–

Homogeneous
goods
Process innovation
1
Innovation competition





Product versus process innovation
Drastic versus non-drastic innovation
Patent race
Incentives to innovate
Executive summary
2
Research and development

Three levels of research:
–
–
–


fundamental research
applied research with project planning
development of new products and their
commercialization
Innovation of product and process
Three stages
–
–
–
invention
adoption
diffusion
3
Five models
Patent race with respect to process innovation
 Process innovation leads to reduction of
average cost: c  c
 Incentives to innovate for

–
–
–
–
–
benevolent dictator
monopolist
perfect competition
two symmetric firms
two asymmetric firms
4
Benevolent dictator v. monopolist
p
p
p M (c)
p M ( c)
c
c
A
  BD
c
c
x
incentive to innovate
x
MR
5
Drastic v. non-drastic innovation
p
p
p (c )  c
M
Innovator enjoys blockaded
monopoly, p M ( c )  c
p M (c)
p M (c)
c
p M ( c)
p M ( c)
c
drastic
innovation
non-drastic
innovation
c
c
X M (c) X M c 
x
X M (c ) X M c 
x
6
Exercise (drastic or non-drastic
innovation)
Inverse-demand function p=a-X
 All firms have identical unit costs c , where

c  a  2c

Only one firm reduces its unit cost to
c  2c  a
Infer kind of innovation
7
Perfect competition

Incentives to innovate
–
for drastic innovation
 PC ,drastic   M c   0   M c    M c    A
–
for non-drastic innovation
c
 PC ,nondrastic  c    c D c      D c dc
c
 A   PC ,nondrastic   BD
(compare next slide and slide „ Benevolent dictator v.
monopolist”)
8

PC ,nondrastic
graphically
p
c
 PC, nondrastic
c
X c 
X
9
Assumptions and notation for
dyopolistic innovation competition
Patent race with respect to process innovation
 R&D expenditure of firms 1 and 2: F1 and F2
 A measure of innovation difficulty : F0


Innovation probability of firm i:

Probability of no innovation:
Fi
wi 
F0  F1  F2
F0
w
F0  F1  F2
10
Exercise (innovation probability)
How does the innovation probability
depend on F0 , F1 and F2.
F1
F2
½ F0
6F0
34F0
100F0
F0
½ F0
F0
F0
F0
0
w1
Innovation
probability of firm 1
11
Symmetric innovation competition
F1
F2
1
2
Initially, none of the firms is
in the market. The successful
firm enters the market and
receives  M .
12
Equilibrium (symmetric case)

Profit function of firm 1
F1
1 F1 , F2  
 M  F1
F1  F2  F0

Reaction function of firm 1
F1R ( F2 )   M F2  F0   F2  F0 

Nash equilibrium
F1N , F2N , F1N  F2N   1 F0  1  1  M  1
 F1N F2N

0

F0
 F0
2
with
24
F1N F2N

M

 M
 M  M  8F0 
4


 0

13
F2
 M  F0
F1R ( F2 )
Nash equilibrium
F2R ( F1 )
 M / 4  F0
 M / 4  F0
 M  F0
F1
Exercise (sequential symmetric case)
Consider the symmetric case with F0=0.
Calculate an equilibrium in the sequential
game:
F1
F2
1
2
1
S. :   M , F2R 
4

15
Asymmetric case: one incumbent,
one potential competitor



F1
F2
p1
p2
1
2
Monopolist (firm 1) with
average cost c , and potential competitor (firm 2)
Process innovations leads to reduction of average
cost: c  c
Profits, net of R&D expenditure M
–
No firm innovates
1   (c ), 2  0
–
Established firm innovates
1   M (c),  2  0
–
Entrant innovates (price competition)
1    0
d
1
and
 a2 , non - drastic innovation
2     b
 2 , drastic innovation
d
2
16
Profit functions (asymmetric case)

Profit function of firm 1 (monopolist)
F1
F2
M
 1 F1 , F2  
 c  
 1d 
F1  F2  F0
F1  F2  F0
F0

 M c   F1
F1  F2  F0

Profit function of firm 2
F2
 2 F1 , F2  
 d2  F2
F1  F2  F0
17
Incentives to innovate
No firm
innovates.

A
2

A
1

GN
1
Entrant
innovates.

GN
2
Monopolist
innovates.
18
Replacement effect (Arrow)
The Arrow terms are defined as the profit
differences a firm enjoys by innovating rather
than not innovating.
 If the incumbent innovates, he replaces
himself. If the entrant innovates, he achieves
positive profits as compared to zero profits:

1A   M c    M c    d2  0   2A
 a2  c  c   X c , non - drastic innovation
   b
M
c ,



drastic innovation
 2
d
2
19
p
p
p M (c)
p M (c)
c
p M (c)
M
p ( c)
drastic
innovation
c
nondrastic
innovation
c
c
x
Incentive to innovate
from replacement
effect

A
1
 2
A
for established firm
for potential competitor
x
Efficiency effect (Gilbert, Newbery)
The Gilbert-Newbery terms are defined as
the profit differences a firm enjoys if she
herself rather than her competitor innovates.
 The established firm’s incentive to remain a
monopolist is greater then the entrant’s
incentive to become a duopolist:

1GN   M c   1d   d2  0   GN
2
21
Gilbert-Newbery effect: 1d  d2  M (c)
From previous slide follows: 1d   d2   M (c) 1
Drastic innovation firm 2
1d  0 and d2   M (c)
Nondrastic innovation firm 2
1d  0 and  2d   2a  c  c   X c    M (c)
blockade and ”=”
in equation (1)
deterrence and ”<”
in equation (1)
 equation on previous slide is true
22
Replacement versus efficiency
effect

Replacement effect
–
entrant has a greater
incentive to innovate
  
A
1
A
2

Efficiency effect
–
established firm has a
greater incentive to
innovate

GN
1
 
GN
2
23
Equilibrium (asymmetric case)

Reaction function of firm 1
F1R ( F2 )  F2  F0   F0  M c    M c   F2  M c   1d 
 F2  F0   F0 1A  F2 1GN

Reaction function of firm 2
F2R ( F1 )  F1  F0  
F0  F1  d2
 F1  F0   F0  2A  F1 GN
2

Nash equilibrium: “forget it“
24
Identifying the replacement effect

The greater the monopoly’s profit without
innovation, the less are the monopolist’s
incentives to innovate:
F1R
 c 
M
0
25
Special case: efficiency effect only

Hypothesis: F0 = 0
i.e., it is certain that one of the two firms innovates

Reaction function of firm 1
F1R ( F2 )   F2  F2 (  M c   1d )

Reaction function of firm 2
F2R ( F1 )   F1  F1 d2 c 

Nash equilibrium:
M
d
d
M
d
d 
 M




(

c


)

(

c


)

d
d
1
2
1
2 
 (  c   1 )
;

2
M
d
d 2
M
d
d 2

 c   1   2 
 c   1   2  

26
Executive summary I




The higher the attainable monopoly profit, the
higher the expenditures for R&D in the patentrace Nash equilibrium.
The less likely successful innovation, the less all
firms’ expenditures for R&D.
R&D expenditures might be strategic
complements or strategic substitutes.
Sometimes, it may pay for the monopolist to file a
patent but not to actually use it himself (sleeping
patent).
27
Executive summary II
Incentives to innovate for the asymmetric duopoly:


If the incumbent innovates, he replaces himself. If
the entrant innovates, he achieves positive profits as
compared to zero profits.
 replacement effect
The established firm’s incentive to remain a
monopolist rather than becoming a duopolist is
greater then the entrant’s incentive to become a
duopolist.
 efficiency effect
28
Innovation competition with spillover effect
Basic idea
 Simultaneous quantity competition (2nd stage)
 Simultaneous R&D competition (1st stage)
 Simultaneous R&D cooperation (1st stage)
 Comparison of R&D competition and R&D
cooperation
 Executive summary

29
Basic idea

It is often not possible to internalise the
benefits of R&D activities perfectly:
–
–

employee turnover
analysis of patents
R&D cooperation can be observed in some
industries (e.g. PSA has different cooperation
projects). On the product market, the firms
may still compete.
30
The model


Before the innovation c  c1  c2
The innovation reduces costs by
c1  F1  F2
c  c1
to
c2  F2  F1
c  c2

 measures the spill-over effect.

Fi...R&D activity; C(Fi)...costs of R&D activity
Structure

F
1
F
2
x1
x2
1
2
31
Profit function
Profit functions
1 F1 , F2 , x1 , x2   a  bX  c  c1 x1  C F1 

 2 F1 , F2 , x1 , x2   a  bX  c  c2 x2  C F2 
assume: a  c  1 and b  1
1 F1 , F2 , x1 , x2   1  c1  x1  x2 x1  C F1 
 1  F1  F2   x1  x2 x1  C F1 
 2 F1 , F2 , x1 , x2   1  c2  x1  x2 x2  C F2 
 1  F2  F1   x1  x2 x2  C F2 
32
Cournot competition (2nd stage)

Reaction functions
1  c1  x2 
1  c2  x1 
R
R
x1  x2  
and x2  x1  
2

2
Cournot equilibrium
1  2c1  c2  1  2   F1  2   1F2
C
x1 F1 , F2  

3
x2C F1 , F2  analogous

3
Reduced profit functions
 F1 , F2   


C
1
1 2 c1  c2 2
3
 C F1 
C
2
1 2 c2  c1 2
3
 C F2 
 F1 , F2   
33
How Cournot outputs depend on

„real“ R&D activity ci :
x
 0 and
ci
C
i

x Cj
ci
0
R&D activity Fi :
xiC 2  

0
Fi
3
2   1  0,   12


Fi
3  0,   12
x Cj
34
Exercise (R&D competition on
st
1 stage)

Assume C Fi   12 Fi 2 i  1,2.
Find the symmetric equilibrium in the R&D
game.
S. : F  F 
N
1
N
2
2 2  
9  2 1   2   
35
Analyzing direct and indirect
effects (R&D competition) I
1C F1   1 F1 , x1C F1 , x2C F1 
 C2 F1    2 F1 , x1C F1 , x2C F1 
Influence of F1 on firm 1’s profit
d 1C  1  1 dx1C  1 dx2C



dF1
F1 x1 dF1 x2 dF1
direct
effect
 1
C F1 
 x1C 
F1
F1
=0
=0
>0
<0
x2C 2   1  0,   12


F1
3  0,   12
1
strategic 0,   2

effect  0,   12
36
Analyzing direct and indirect
effects (R&D competition) II

Influence of F1 on firm 2’s profit
d C2  2  2 dx2C  2 dx1C



F1 x2 dF1 x1 dF1
dF1
direct
effect
 x
>0
C
2
=0
=0
?
strategic effect
2
x
3
C
2
<0
1


,
0


2
4
2
     x2C 
3   0,   12
3
37
Exercise (R&D cooperation on
st
1 stage)
We assume that firms cooperate on the first
stage and compete on the second. Therefore:
 Firms want to maximize the joint reduced profit function  C F1 , F2  : 1C F1 , F2    C2 F1 , F2 .
 While assuming the same quadratic cost function as before, calculate the cartel solution.

S. : F1K  F2K  9 2211 2
38
Profit comparison of R&D
competition and R&D cooperation
i
 iK
 iN
 0
  0.5
 1

39
Analytical comparison of
competition v. cooperation
Does R&D competition yield higher R&D
activities than cooperation?
 In our concrete model, we find

F1N  F2N  F1K  F2K 
22   
21   


9  21   2    9  21   2
 0 ,   12

1

0
,



2
40
Graphical comparison of
competition v. cooperation
Fi
Fi K
Fi N
 0
  0.5
 1

41
Interpreting the comparison by
way of external effects
The influence of firm 1 on firm 2’s profit is
an external effect; see slide „Analyzing direct
and indirect effects (R&D competition) II“
 We found

K
N
1


0
,



neg.
ext.
effect
F

F
 2  2 dx
i
i
2


F1 x1 dF1  0,   12  pos. ext. effect Fi K  Fi N
C
1

Bingo!
42
Executive summary: If spillover
effects are sufficiently important,
Firms want to underinvest in R&D for
strategic reasons;
 Firms want to cooperate in order to prevent
suboptimal R&D activities;
 Governments may allow R&D cooperation
in order to enhance R&D activities.

43