Geography Reference
In-Depth Information
leaping toward
s*
- may know which components are 'right' and which are 'wrong'.
These benei ts rel ect both the more accurate transmission the close actor receives
originally and his or her ability to consult with the owner of the template while trying to
correct the original transmission.
Interdependence and the landscape
Much of the intuition of the results l ows from an understanding of the impact of
K
on
the topography of the typical landscape. Four ef ects strike us as especially germane.
3
First, as
K
increases, the landscape shifts from being smooth and single-peaked to being
rugged and multi-peaked. When
K
= 0, the
N
components contribute independently
to knowledge utility. In that situation, alteration of a single component changes the
contribution of that component alone. From any initial location on a landscape, then,
a close or distant actor can climb to the global peak via a series of utility-improving,
single-component tweaks to its knowledge. In contrast, when
K
=
N
− 1, every com-
ponent inl uences the contribution of every other component. Then a small step on the
landscape - a change in a single component - alters the contributions of all
N
compo-
nents. Consequently, adjacent pieces of knowledge have altogether uncorrelated utilities,
producing a very rugged surface with many local peaks.
Second, as
K
rises, not only do local peaks proliferate, but also the height of the average
peak declines. As the web of connections across components thickens, it becomes possi-
ble to exhaust opportunities for incremental improvement even at low levels of perform-
ance. Hence, interdependence decreases the fruitfulness of incremental search.
Third, though the height of the average peak falls as
K
rises, the heights of the highest
peaks rise with
K
. When components interact with one another more richly, the amount
of variety attainable by mixing and matching components increases, and the quality of
the best combination within that variety improves. Rugged landscapes, though chal-
lenging to navigate, of er greater fertility than smooth ones - in other words, they more
likely produce at least one exceptional peak. More mechanically, recall that we drew a
contribution C
j
for each possible realization of (
s
j
;
s
j
1
,
s
j
2
, . . .,
s
jK
). The number of possible
contributions for each component (2
K
+1
) rises sharply with
K
, increasing the available
variety.
Finally, as
K
increases, the high peaks on the typical landscape spread apart from one
another, shifting from a situation in which peaks cluster in mountain ranges to one in
which peaks spread uniformly across the terrain.
4
With greater interdependence, high
peaks carry less and less information about the location of other high peaks. This ef ect
undermines long-jump search, decreasing the likelihood that a jump that aims for but
misses the global peak will nonetheless land on high ground.
Simulations and results
Percentage of template performance attained
We explored the model under a wide
variety of assumptions regarding
d
close
,
d
distant
, q
close
, and q
distant
. (
N
= 12 throughout.
All results average over 100-200 landscapes.) Results remained similar throughout the
parameter space so we report only a handful of representative cases here (see Rivkin,
2001, for further robustness checks). Figures 15A.1-15A.3 show, as a function of
K
, the
utility attained by the close actor and the distant actor as a percentage of the utility of the
