NK-models. DIMETIC, Maastricht, 15 Oct Koen Frenken

Transcription

1 NK-models DIMETIC, Maastricht, 15 Oct 2008 Koen Frenken

2 Structure of the talk Introduction to NK-model Innovation classification using the NKmodel Decomposable systems and the example of the Wright Brothers inventing the airplane Constructional selection as a model of the emergence of a technological paradigm

3 Properties of the NK-model N stands for the number of elements in a system (genes, routines, technological subsystems) K stands for the number of interdependencies between components with range: 0 K N-1 The number of possible strings, called design space or state space or possibility space: S = 2 N Number of local optima for K=N-1 can be derived analytically as: # = 2 N /(1+ N) The fitness of local optima tends towards the mean for increasing K and N (complexity catastrophe) Fitness of the one global optimum increases for increasing K and N For decentralised search, NK-model transforms into a game with random payoffs

4 Innovation types Henderson/Clark 1990 ASQ - Incremental - Modular - Architectural - Radical Imitation - Success of imitation decreases with K - Supports the resource/competence-based theory of the firm see: K. Frenken (2006) Innovation, Evolution and Complexity Theory (Edward Elgar)

5 System architectures (Altenberg 97)

6 Block maps and decomposability Given that local optima exists, finding the global optimum generally requires exhaustive search involving 2 N trials Except for block maps, which are decomposable If complexity refers to problem-solving difficulty, K is not always a reliable complexity indicator

7 Testing the glider subsystem

8 Testing the system as a whole

9 Doing it Wright

10 Generalised NK-model (Altenberg 97) NK-model has two restrictions: Number of elements equal the number of fitness components (each element is assumed to have its own fitness) The fitness component of each element is affected by the same number (K) other elements Dropping these assumptions gives use the generalised NK-model in which: Each element affects one or more fitness components Each fitness component is affected by one or more elements These relations make up the genotype-phenotype map (compare Saviotti-Metcalfe 84 RP)

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12 Example of a genotype-phenotype map/architecture

13 Generalised model allows to model systems growing in size

14 System growth and constructional selection as a model of technological paradigms See more Altenberg 1994 and Frenken 2006

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16 Conclusions Generalised NK-model can be used to model complex systems that grow in size, both in design space and in function space Constructional selection explains the emergence of technological paradigms characterised by a core elements with high pleiotropy and peripheral elements with low plieotropy Core elements are selected early on and then become frozen: a lock-in process without increasing returns Paradigms adapt by adding new elements or mutating peripheral elements Applications in environmental innovation policy

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20 24. Siggelkow, N., Rivkin, J.W., When Exploration Backfires: Unintended Consequences of Multi-Level Organizational Search. Academy of Management Journal 49, Simon, H.A., Near decomposability and the speed of evolution, Industrial and Corporate Change 11(3), Solow, D., Vairaktarakis, G., Piderit, S.K., Tsai, M., Managerial Insights into the Effects of Interactions on Replacing Members of a Team, Management Science 48(8), and empirical work loosely inspired by NK such as work on: - technological complexity and patent citations (Fleming 2001; Fleming and Sorenson 2001, 2004), - vertical integration (Sorenson 2003), - automation in the late nineteenth century (Reinstaller and Holzl 2004), - technological complexity and social networks (Fleming et al. 2006), - national financial systems (Holzl 2006) and many unpublished manuscripts