Competing Technologies, International Diffusion and the Rate of Convergence to a Stable Market Structure

This paper is motivated by two 'stylized facts' concerning the dynamics of diffusion of different technologies competing for the same market niche. a) A stable pattern of market sharing with no overwhelming dominant position is rarely observed in markets with network esternalities. Unbounded increasing returns to adoption are often called for an explanation of this fact. However the argument is generally based on an incorrect interpretation of the Brian Arthur (1990) model. As we show with a simple counterexample unbounded increasing returns are either necessary nor sufficient to lead to technological monopolies even in a stable external environment. b) International diffusion may lead sometimes to different standards in different countries ( the archetypal case is the diffusion of typewriter-computer keyboards - AZERTY vs. QWERTY) or to the diffusion of the same standard in every country (the archetypical example being VCRs - Beta vs. VHS), even without intervention of any regulatory agency. Intuitively when convergence to the same standard is not an accident of history, it is an outcome of the relative weight of international spillovers as compared to nationwide esternalities. The crucial question is: can a model that account for the former fact accommodate also the latter? In this paper, by establishing some mathematical properties of generalized urn schemes, we build on a class of competing technology dynamics models to develop an explanation for the former "fact" and to provide sufficient conditions for convergence to the same or to different technological monopolies in different countries. Our explanation for the empirical tendency to converge to technological monopoly relies on convergence rate differentials to limit market shares: We show that a market can approach a monopoly with a higher speed than it approaches any feasible limit market share where both technologies coexist. Convergence to market sharing, we conclude, is in general so slow that the environment changes before the market share trajectory becomes stable in a neighborhood of its limit. The empirical implication is that among markets with high rate of technological change and increasing returns to to adoption, a prevalence of stable monopolies over stable market sharing should be expected.