THE POWER
OF
IMPERFECT IMITATION
Hart E. Posen, University of Michigan
Joint work with:
Jeho Lee, Seoul National University
Sangyoon Yi, Kaist / Univ. of Michigan
A NAÏVE INTUITION TELLS US…
…the performance of
imperfect imitation will
be somewhat less than
that which may be
garnered by perfect
imitation of market
leaders.
We argue that the opposite is true…
2
ALCHIAN CONJECTURE
“While there certainly are those who consciously
innovate, there are those who, in their imperfect
attempts to imitate others, unconsciously
innovate
by
unwittingly
acquiring
some
unexpected or unsought unique attributes which
under the prevailing circumstances prove partly
responsible for the success.”
(Alchian 1950: p. 218-219)
3
IMPERFECT IMITATION
Intellectual
Property
Bounded
Rationality
4
BOUNDED RATIONALITY – SIMON (1957)

Actual behavior departs from rationality
assumption (Simon 1957: p. 81)
“Rationality requires a complete knowledge and anticipation
of the consequences that will follow on each choice.”
 “(Future) values can be only imperfectly anticipated.”
 “Rationality requires a choice among all possible alternative
behaviors…only a very few of all these … ever come to mind.”


Under bounded rationality, the firm satisfies
rather than optimizes
5
UNDER FULL RATIONALITY, IMITATION
IS TRIVIAL…

Given bounded rationality, imitation is not easy.

Many firms are potentially targets of imitation more than can be examined.


Firms sample a subset of the population in deciding whom
to imitate.
Given the target identified, there are many potential
policy decisions that could be imitated – but limited
understanding of cause-effect relationships.

Firms make errors in deciding which elements of the
imitatee’s decisions are worth imitating.
6
CENTRAL RESEARCH QUESTION
Is imitation hindered or helped
by bounded rationality?
7
COMPUTATIONAL MODEL
Perfect Imitation
reality:
t=1
t=2
■■■
■■■
①■□■
(1,2,3,4)
①■□■
②■□□
(1,2,3,4)
②■□■
③□■□
(1,2,3,4)
③■□■
④□□■
(1,2,3,4)
④■□■
Parameters: m = 3, s = 1, N=4, bs = 4, p = 1
Simple
Model
--Firms are
heterogeneous
in their initial
knowledge.
--They engage
in search to
find good
solutions.
--Search
happens only
via imitation.
8
COMPUTATIONAL MODEL
Imperfect Imitation
Examine limited set of firm - Imitate decisions with error
reality:
t=1
t=2
t=3
■■■
■■■
■■■
①■□■
(2,3)
①■□■
(3,4)
①■□■
②■□□
(3,4)
②■■□
(1,3)
②■■■
③□■□
(1,4)
③□□□
(1,4)
③■□□
④□□■
(1,2)
④■□■
(2,3)
④■■■
Parameters: m = 3, s = 1, N=4, bs = 2, p = 0.33
9
IMITATION PERFORMANCE
UNDER
BOUNDED RATIONALITY
100
90
bs == 11 (random)
bs
bs == 55
bs
80
bs == 50
50
bs
perfect
perfect
avg. diversity = 0.19
Performance
70
60
avg. diversity = 0.11
50
40
30
avg. diversity = 0.06
20
avg. diversity = 0.34
10
0
0
10
20
30
40
50
60
70
80
90
Time
10
IMITATION PERFORMANCE
UNDER
BOUNDED RATIONALITY
Bounded Rationality
seems to improve the
efficacy of avg.
imitation.
diversity = 0.19
Why?
100
100
bs == 11 (random)
bs
bs == 55
bs
90
90
80
bs == 50
50
bs
perfect
perfect
80
Performance
Performance
70
70
60
5060
avg. diversity = 0.11
4050
3040
2030
avg. diversity = 0.06
10
20
0
avg. diversity = 0.34
10
bs=1
random
(bs = 1, p=0.3)
0
0
10
20
bs=5
imperf
ect
(bs = 5, p=0.3)
30
40
bs=50
near
perf ect
(bs = 50, p=0.3)
50
60
perfect
ect
perf
(bs = 50, p=1)
70
80
90
Bounded Rationality
Time
Worst performance
with random imitation
Moderate level of
bounded rationality
leads to superior
average performance
Perfect imitation leads
to only moderate
performance.
11
QUANTITY OF DIVERSITY
IN POPULATION
Quantity of diversity
does not fully explain
the result.
Why?
0.50
Average Diversity
0.40
Conjecture
Differences in the
quality of diversity
0.30
0.20
0.10
0.00
bs=1
random
(bs = 1, p=0.3)
bs=5
imperf
ect
(bs = 5, p=0.3)
bs=50
near
perf ect
(bs = 50, p=0.3)
perfect
ect
perf
(bs = 50, p=1)
Bounded Rationality
12
QUALITY OF DIVERSITY
MEASURE OF USEFUL KNOWLEDGE IN POPULATION
■ ■ ■
Reality
Firms:
①
■ □ □
②
■ □ ■
③
□ □ ■
Is there a useful
bit of knowledge
in population?
Yes
No
Yes
=
2/3
13
QUALITY OF DIVERSITY
LEVEL OF USEFUL KNOWLEDGE IN POPULATION
What is the useful
knowledge that is lost?
100
Level of Useful Knowledge
90
80
70
60
50
bs
bs = 5
bs
bs = 50
40
perfect
perfect
30
0
10
20
30
40
50
60
70
80
90
Time
Perfect (and near) imitation are
poor at maintaining useful
knowledge. 30-40% is rapidly lost.
Imperfect imitation
maintains the largest share of
useful knowledge.
14
A CONTROLLED EXPERIMENT
MEASURE OF PERCOLATION OF USEFUL KNOWLEDGE
Reality
Firm 1
Firm 2
Firm 3
Firm 4
■■■■■ … ■
□■■□□ … ■
□■□■■ … □
□□■□■ … ■
■□□□□ … □
Is the useful
knowledge
copied?
Probability of
Being Copied
Good idea in a bad firm
15
A CONTROLLED EXPERIMENT
5
Good Idea in a Bad Firm
The useful knowledge
that is lost by near
perfect imitation is
‘good decisions in bad
firms’
4
3
2
1
0
bs=1
random
(bs = 1, p=0.3)
bs=5
imperfect
(bs = 5, p=0.3)
bs=50
perf ect
near
perfect
perfect
(bs = 50, p=0.3) (bs = 50, p=1)
Bounded Rationality
Number of Firms Preserving the Unique Bit
Number of Firms Preserving the Unique Bit
PERCOLATION OF USEFUL KNOWLEDGE
20
Good Idea in a Good Firm
15
10
5
0
bs=1
random
(bs = 1, p=0.3)
bs=5
imperfect
(bs = 5, p=0.3)
bs=50
perf ect
near
perfect
perfect
(bs = 50, p=0.3) (bs = 50, p=1)
Bounded Rationality
16
Good Firm
Bad Firm
17
Good Firm
Bad Firm
18
FINDINGS & CONTRIBUTIONS

Imperfect imitation is more powerful than perfect
imitation.

Perfect imitation rapidly eliminates useful knowledge from the
population.



When good ideas happen to bad firms…
Quality of variation matters – as much as quantity.
Simon argued that actual behavior of economic agents
deviates from the rationality assumption.

We show that there is an adaptive role in such deviation.
19