Imitation, Proximity, and Growth - A Collective Swarm Dynamics Approach

This paper is based on the premise that economic growth is driven by an interplay between innovation and imitation in an economy composed of interacting ̄rms operating in a stochastic environment. A novel approach to modeling imitation is presented based on range-dependent processes that describe how ̄rms consider proximity when imitating peers who are found in a given neighborhood in terms of productivity. Using a particularly tractable approach, we are able to analyze how drastically di®erent economic growth scenarios emerge from di®erent im- itation strategies. These emerging scenarios range from di®usive growth where the variance of productivity grows inde ̄nitely, to balanced growth described by a traveling wave with ̄xed variance. The latter scenario is sustained only when imitation strength among ̄rms exceeds a critical bifurcation threshold.