Analytical Investigation of Innovation Dynamics Considering Stochasticity in the Evaluation of Fitness

Physical Review E, Vol. 71, 2005

4 Pages Posted: 14 Feb 2007

See all articles by Dirk Helbing

Dirk Helbing

ETH Zürich - Department of Humanities, Social and Political Sciences (GESS)

Martin Treiber

Dresden University of Technology - Institute for Transport and Economics

Nicole J. Saam

University of Erfurt

Abstract

We investigate a selection-mutation model for the dynamics of technological innovation,a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success (fitness), they are an essential prerequisite for innovation. Together with a selection of above-average technologies due to imitation behavior, they are the driving force for the continuous increase in fitness. We will give analytical solutions for the probability distribution of technologies for special cases and in the limit of large times.

The selection dynamics is modelled by a proportional imitation of better technologies. However, the assessment of a technology's fitness may be imperfect and, therefore, vary stochastically. We will derive conditions, under which wrong assessment of fitness can accelerate the innovation dynamics, as it has been found in some surprising numerical investigations.

Suggested Citation

Helbing, Dirk and Treiber, Martin and Saam, Nicole J., Analytical Investigation of Innovation Dynamics Considering Stochasticity in the Evaluation of Fitness. Physical Review E, Vol. 71, 2005. Available at SSRN: https://ssrn.com/abstract=960227

Dirk Helbing (Contact Author)

ETH Zürich - Department of Humanities, Social and Political Sciences (GESS) ( email )

ETH Zurich - Swiss Federal Institute of Technology
Clausiusstrasse 50
Zurich, 8092
Switzerland

HOME PAGE: http://www.coss.ethz.ch

Martin Treiber

Dresden University of Technology - Institute for Transport and Economics ( email )

Mommsenstrasse 13
D-01062 Dresden
Germany

Nicole J. Saam

University of Erfurt ( email )

Faculty of Economics, Law and Social Sciences
Nordhäuser Str. 63
D-99089 Erfurt
Germany

HOME PAGE: http://www.uni-erfurt.de/esf

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