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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
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