Dynamic increasing returns and innovation diffusion: bringing Polya Urn processes to the empirical data

Abstract

The patterns of innovation diffusion are well approximated by the logistic curves. This is the robust empirical fact confirmed by many studies in innovations dynamics. Here we show that the logistic pattern of innovation diffusion can be replicated by the time-dependent stochastic process with positive feedbacks along the diffusion trajectory. The dynamic increasing returns process is modeled by generalized Polya urns. So far, urn models have been mostly used to study the [path-dependent] limit properties. On the contrary, this work focuses on the transient [finite time] properties studying the conditions under which urn models capture the logistic trajectories which often track empirical diffusion process. As examples, we calibrate the process to match several cases of diffusion of motor ships in European countries.

International trade and technological competition in markets with dynamic increasing returns

“…1 The rst applications of Pólya urns in economics date back to the seminal works by Simon (1955), Ijiri and Simon (1975) and Ijiri and Simon (1977) on rm size distribution. Since then, Pólya urn processes have been employed in several domains of economics, and in particular in the analysis of technical change (Arthur et al, 1987;Arthur, 1989;Dosi et al, , 2019 and industry dynamics (Fu et al, 2005;Bottazzi and Secchi, 2006a;Bottazzi et al, 2007;Riccaboni et al, 2008). 2 However, to the best of our knowledge, so far there is no application of Pólya urns to the analysis of international trade dynamics.…”

“…Phelps and Winter, 1970;Bils, 1989;Rotemberg and Woodford, 1991;Greenwald and Stiglitz, 2005). Furthermore, the assumption that the probability of competing for a market opportunity is an increasing function of market size captures the essence of dynamic increasing returns in market selection (see Arthur, 1989;Dosi et al, 2019), and it is a proxy for the fact that bigger rms have better distribution channels and are thus more likely to be known among costumers. Finally, competition over the e ciency domain captures the fact that relatively more productive rms are able to charge a lower price and to attract a higher number of consumers, increasing their market shares (Dosi et al, 1995(Dosi et al, , 2017).…”

The perils of pleasing: Innovation-stifling effects of customized service provision

“…This study contributes to the (service) innovation strategy and management studies literature by elaborating specific conditions that can explain the outcomes from investing in customer-sensing capabilities. The rare combination of simulations and initial empirical tests has allowed us to highlight certain boundary conditions that nurture myopic innovation (Ganco 2017;Dosi et al 2019;Baumann et al 2019). A second contribution is specific to the literature on the innovation of customized services (Visnjic Kastalli and Van Looy 2013;Cabigiosu and Campagnolo 2019).…”

Interacting discovery processes on complex networks

“…The gray area up to T = 10 4 corresponds to the values of (a-e). typical of empirical trajectories of diffusion process [74], here are strongly influenced by the topology of the network. This can be seen by comparing the two β 1 (t) of Fig.…”