Applications of the NKmodel

1
Applications of the NK-model

• Koen Frenken
• URU, Utrecht University, The Netherlands
• ETIC and SIME
• 2 April 2004

2
Structure of the lecture

• Appreciative theorising and formal modelling
• A short review of evolutionary models and their
  use
• NK-model (Kauffman 1993)
• Theoretical applications of the NK-model
• Empirical applications of the NK-model
• Discussion

3
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

4
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)

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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

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NK-model (Kauffman 1993 Levinthal 1997)

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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 (Kauffmans
  complexity catastrophe)

8
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.

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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 co-exist (reflecting local optima).
  Demythologises simple linear succession history

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References

•  
• 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/Working20P
  apers/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.