Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-01-10
Physical Review E 71, 067101 (2005)
Physics
Condensed Matter
Statistical Mechanics
For related work see http://www.helbing.org
Scientific paper
10.1103/PhysRevE.71.067101
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.
Helbing Dirk
Saam Nicole J.
Treiber Martin
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