Selforganization of R

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Self-organization of RD search in complex
technology spaces Gerald Silverberg and Bart
Verspagen MERIT, Maastricht University
ECIS, Eindhoven University of Technology
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Stylized Facts About Technological Change
  1. Technical change is cumulative new
technologies build on each other.   2.  Technical
change follows relatively ordered pathways, as
can be measured ex post in technology
characteristics space (see the work of Sahal,
Saviotti, Foray and Gruebler, etc.). This has led
to the positing of natural trajectories (Nelson),
technological paradigms (Dosi), and technological
guideposts (Sahal).   3.  The arrival of
innovations appears to be stochastic, but more
highly clustered than Poisson (overdispersion).
  4.  The size of an innovation is drawn from
a highly skewed and possibly fat-tailed
distribution.   5.  Technological trajectories
bifurcate and also merge.   6.  There appears to
be a certain arbitrariness in the path actually
chosen, which could be the result of small events
(path dependence or neutral theory?) and cultural
and institutional biases (social construction of
technology?).   7.  Incremental improvements tend
to follow upon radical innovations according to
rather regular laws (learning curves).
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Skewness indicators of various innovation
datasets(Source Scherer et al. 2000,
Uncertainty and the size distribution of rewards
from innovation, JEE)
 
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Innovation Size Distributions (Pareto Plots)
Based on Patent Citations
EPO 1989 patent citations (left) and USPTO 1989
patent citations (right)
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Innovation Size Distributions (Pareto Plots)
Based on Monetary Value
Harvard patent license fees (left), NL patent
valuation survey (middle), UK patent valuation
survey (right)
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The Hill Estimator
Placing the n observations Xi in descending order
and denoting the resulting rank-order statistics
by Xi, X1?X2? ?Xn, the Hill estimator is
defined as
k H(k,n) 1/k ? (ln Xi
ln Xk1 ).
ML Estimator on Grouped Data
Data are counts of number of observations ni in
bins Lc, L1), L1, L2), , Lm-1, Lm), Lm,
?). The log likelihood function is then
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The Tail, its Fatness, and its Width(estimated
using a data-driven Hill estimator, Silverberg
and Verspagen 2004)
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Percolation diagram in technology-performance
space. Lattice sites are filled at random. A site
is viable when it connects to the baseline.
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Probability of a random site being on the
infinite cluster P as a function of the
percolation probability q
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New innovations are generated with probability p
in a region d units above and below the
technological frontier.
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A cluster of simultaneous invention occurs when a
disjoint island of invention is suddenly joined
to the frontier by a single 'cornerstone'
innovation.
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Screen Shot of Run with Search Radius 6
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Whats New in the New (Self-Organizational) Model

• Toyota principle Nothing is impossible.Instead
  of 0, 1 random values for site feasibility, we
  now draw a difficulty value q from a LN(ltqgt, s)
  distribution. High skewness of LN, however, makes
  some sites very difficult.
• Firms now dig out the site, with complete
  technological spillovers between periods qi(t1)
  max(0, qi(t)-B?), where ? is drawn from a
  uniform distribution on 0, 1).
• We now allow myopic strategic firm behavior
  firms position themselves within their
  technological search neighborhoods, moving with
  highest probability to the site which is highest
  on the BPF based on multinomial transition
  probabilities.
• Firms now profit from successful innovations,
  with their RD budgets increasing in proportion
  to their innovation harvest.

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Firms Move by Myopically Searching for Higher
Positions within their Column n-Neighborhood on
the BPF before Untertaking Next RD Round
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Innovation Rate Switching between the Two Regimes
as a Function of the Search Radius m and ltqgt
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Innovation Rates in the Two Regimes as a Function
of s
Fig. 5 The innovation rate as a function of the
standard deviation, for ltqgt0.4, m3, one data
point per value.
Fig. 4 The innovation rate as a function of the
standard deviation of the generating lognormal
distribution, five data points per value, for
fixed and moving firm regimes. ltqgt2, m3.
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Evolution of Firms Clustering Coefficient for
ltqgt1, s5, m3.
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Moving Firms Clustering Coefficient as a
Function of Search Radius m and ltqgt (10 data
points per value)
Clustering measure
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Innovation Size Distribution, Fixed
Firms,ltqgt0.2, s4, m3
Hill Estimator
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Innovation Size Distribution, Moving Firms,
ltqgt0.2, s4, m3
Hill estimator
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?Amazing Fact!?These innovation size
distributions for moving firms look the same
(a?1, scaling over more than two decades) for any
parameter values (at least until now).SOC??
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More Pareto Plots for the SO Regime, varying s
b
a
   
c
Fig. 11 Pareto plots of runs with ltqgt0.4, m3,
?1, and ? (a) 2, (b) 3, (c) 5.
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More Pareto Plots, varying p
a
b
Fig. 12 Pareto plots for ltqgt0.4, m3, s2, and
(a) p0, (b) p1.9.
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Scaling in the Variance of BPF vs Innovation Rate
Graph
Fig. 14 Scatter plot of variance of BPF vs.
innovation rate for ltqgt1, m3, ?1, and various
values of ? between 0 and 11, pooling multiple
runs.
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Conclusions

• Introduction of moving, myopically rational
  firms (self-organizational regime) results in
  power-law distribution of innovation sizes with
  tail exponent a1 (as compared to skewed but not
  fat-tailed distribution for fixed firms)
• This result is insensitive to parameter values
  gt self-organized criticality?
• The self-organized regime yields higher rates of
  innovation than for fixed firms for lower ltqgt
  (mean of lognormal seeding distribution), higher
  s (standard deviation of lognormal distribution)
  and higher p (payoff for previous innovations)
• Scaling relationship between unevenness of
  innovation across sectors and rate of innovation
  for variable s but not ltqgt?