Geography Reference
In-Depth Information
unspecii ed: how we generate landscapes and how actors search to rediscover the original
success.
Generation of landscapes
Each piece of knowledge consists of
N
components, and
each component
j
,
j
[ {1, 2, . . .,
N
}, can be coni gured in two ways. Hence a particular
piece of knowledge
s
is an
N
- vector {
s
1
,
s
2
, . . .,
s
N
} with
s
j
[ {0, 1}. In the knowledge
germane to a chemical process, for instance, component
j
might indicate the inclusion or
exclusion of a particular catalyst. Similarly, a string of four components could represent
which of 2
4
= 16 shades a heated mixture must turn before being removed from a l ame.
For any set of components, 2
N
possible pieces of knowledge (recipes) exist. We assign a
utility value to each of these as follows. Assume that each component contributes
C
j
to
utility.
C
j
, depending not only on the coni guration, 0 or 1, of component
j
, but also on
the coni guration of
K
other randomly assigned components:
C
j
=
C
j
(
s
j
;
s
j
1
,
s
j
2
, . . .,
s
jK
).
For each possible realization of (
s
j
;
s
j
1
,
s
j
2
, . . .,
s
jK
), we draw a contribution C
j
at random
from a uniform distribution between 0 and 1. The overall utility associated with a piece
of knowledge, then, averages across the
N
contributions:
U
(
s
) = [
C
j
(
s
j
;
s
j
1
,
s
j
2
, . . .,
s
jK
)] /
N
.
K
, the parameter that governs interdependence, ranges from 0 to
N
− 1.
2
K
= 0 corre-
sponds to a simple situation in which the contribution of each component depends only
on the coni guration of that component.
K
=
N
− 1 captures a complex setting in which
the contribution of each component depends delicately on the coni guration of every
other component.
Once the modeler sets
N
and
K
and the simulation generates a particular landscape
(i.e. a utility
U
(
s
) for each of the 2
N
possible pieces of knowledge), the simulation notes
the piece of knowledge
s*
that produces the greatest utility, which serves as a template in
subsequent search ef orts.
Search
A modeled close actor and a modeled distant actor enter the landscape, and
each struggles to rediscover the original success. Rel ecting the reasoning early in the
main text, neither begins precisely atop the peak at
s*
. Rather, each receives an imperfect
transmission of the ef ective knowledge and begins some distance
d
from
s*
(i.e.
d
of its
N
components dif er from
s*
). It must then correct its understanding through search.
We consider two types of search. A party involved in incremental search adjusts one
component, accepts the adjustment if it produces an improvement in utility, and ceases
to search when no improvement opportunities remain. A party engaged in long-jump
search changes multiple decisions at once, leaping toward
s*
. Its leap typically misses
the target; it replicates each component of
s*
with probability q. q < 1 rel ects imperfect
access to the template. After its leap, the long jumper improves incrementally until it
exhausts opportunities. Note that either type of search could terminate on a local peak,
instead of at
s*
.
Though both parties have imperfect access, the close actor has better access because of
his or her social proximity to the original success, which serves as a template. We model
the impact of social proximity in three ways. The proximate actor may begin the search
closer to
s*
(
d
close
<
d
distant
), leap toward
s*
with greater accuracy (q
close
> q
distant
), or - in