Transcript The role of models in evolutionary economics and

Applications of the NK-model
Koen Frenken
URU, Utrecht University, The Netherlands
ETIC and SIME
2 April 2004
Structure of the lecture
1. Appreciative theorising and formal
modelling
2. A short review of evolutionary models and
their use
3. NK-model (Kauffman 1993)
4. Theoretical applications of the NK-model
5. Empirical applications of the NK-model
6. Discussion
Appreciative theorising and
formal modelling
• Nelson and Winter (1982)
• The evolutionary paradigm as opposed to
neoclassical and institutional economics
• The need to combine appreciative theorising
and formal modelling, i.e. deductive and
inductive reasoning
Three main objectives of simulation
• 1. ‘To aid intuition’ i.e. to come up with
explanations for stylised facts and appreciative
theories (Axelrod 1997)
• 2. To generate empirical hypotheses that can be
put to the test
• 3. To be friendly to history (and unfriendly to
the future)
• Two principles: KISS (keep it simple and
stupid) and TAPAS (take a previous model and
add something)
Useful core models for TAPAS strategy
• Game theory to model strategic interaction
• Replicator dynamics to model competition and
industrial dynamics
• Polya urn models, hypercycles, CA and NN to
model diffusion
• Graph/network theory to model the functioning
and dynamics of networks
• NK-model to model problem-solving in complex
systems
NK-model
(Kauffman 1993; Levinthal 1997)
000:
001:
010:
011:
100:
101:
110:
111:
w1
w2
w3
W
0.5
0.2
0.7
0.6
0.9
0.2
0.5
0.4
0.1
0.2
0.8
0.5
0.5
0.3
0.9
0.8
0.7
0.8
0.6
0.3
0.8
0.4
0.4
0.1
0.43
0.40
0.70
0.47
0.73
0.30
0.60
0.43
010
(0.70)
011
(0.47)
110
(0.60)
111
(0.43)
000
(0.43)
001
(0.40)
100
(0.73)
101
(0.30)
Main properties of the NK-model
• The number of local optima is positively
related to the complexity (K) of a system
• Even for small K, finding the global
optimum requires exhaustive search also
called global search (2N)
• The fitness of local optima tends towards
the mean for large N and K values
(Kauffman’s complexity catastrophe)
Theoretical NK contributions
• Bounded rationality (Frenken, Marengo, Valente 1999)
– In evolutionary worlds survival depends on short run
profits. Local search (leading to local optima) performs
better than global search (required to find the global
optimum). Supports the assumption of local search.
• Imitation of complex strategies (Rivkin 2000)
– The more complex a technology / business, the more
firms need to rely on innovation rather than on
imitation. Supports Resource-based/competence view.
• Technological paradigm (Altenberg 1995; Frenken 2004)
– As the dimensionality of technology grows over time,
early developed components become rigid (e.g.,
gasoline engine). Alternative notion of lock-in.
Empirical NK contributions
• Recombinant search (Fleming & Sorenson 2001)
– K is made operational by a measure of how often two
patent classes have been combines previously. The
more often, the lower the complexity. They then test
whether a large K means large dispersion in success
rate (as measured by citation rate). Radical innovation
can now be understood as innovation by recombining
previously unconnected technologies.
• Steam engine designs (Frenken & Nuvolari 2004)
– They reconstruct the design space, and then analyse
whether the competing technologies substitute or coexist (reflecting local optima). Demythologises simple
linear succession history
References
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Altenberg, L. (1995), ‘Genome Growth and the Evolution of the Genotype-Phenotype Map’, in: W.
Banzhaf and F. H. Eckman (eds.), Evolution and Biocomputation. Springer-Verlag: Berlin &
Heidelberg, pp. 205-259.
Axelrod, R., 1997, The Complexity of Cooperation. Agent-Based Models of Competition and
Collaboration (Princeton University Press, Princeton).
Fleming L, Sorenson O, 2001, Technology as a complex adaptive system: evidence from patent data,
Research Policy 30 (7): 1019-1039
Frenken, K. (2004). Innovation, Evolution and Complexity Theory (Cheltenham UK and
Northampton MA: Edward Elgar), forthcoming.
Frenken, K., L. Marengo, M. Valente, 1999, Interdependencies, nearly-decomposability and
adaptation, in: T. Brenner (Editor), Computational Techniques to Model Learning in Economics
(Kluwer, Boston etc.), forthcoming.
Frenken, K., Nuvolari, A. (2004). The early development of the steam engine: An evolutionary
interpretation using complexity theory, Industrial and Corporate Change 13, forthcoming. Download
at: http://www.tm.tue.nl/ecis/Working%20Papers/eciswp89.pdf
Kauffman, S.A., 1993, The Origins of Order. Self-Organization and Selection in Evolution (Oxford
University Press, Oxford and New York).
Levinthal, D., 1997, Adaptation on rugged landscapes, Management Science 43, 934-950.
Nelson, R.R., en Winter, S.G. (1982). An Evolutionary Theory of Economic Change. Cambridge
Mass.: Harvard University Press.
Rivkin, J.W. (2000). Imitation of complex strategies. Management Science, 46, 824-844.