On singularities in combination-driven models of technological innovation

We provide a theoretical framework to understand when firms may benefit from exploiting previously abandoned technologies and brands. We model for the long run process of innovation, allowing for sustainable diversity and comebacks of old brands and technologies. We present two extensions to the logistic and Lotka-Volterra equations, which describe the diffusion of an innovation. First, we extend the short-term competition to a long-term process characterized by a sequence of...

Technological cumulativeness is considered one of the main mechanisms for technological progress, yet its exact meaning and dynamics often remain unclear. To develop a better understanding of this mechanism we approach a technology as a body of knowledge consisting of interlinked inventions. Technological cumulativeness can then be understood as the extent to which inventions build on other inventions within that same body of knowledge. The cumulativeness of a technology is t...

In this work we analyze how reputation-based interactions influence the emergence of innovations. To do so, we make use of a dynamic model that mimics the discovery process by which, at each time step, a pair of individuals meet and merge their knowledge to eventually result in a novel technology of higher value. The way in which these pairs are brought together is found to be crucial for achieving the highest technological level. Our results show that when the influence of r...

Functional technical performance usually follows an exponential dependence on time but the rate of change (the exponent) varies greatly among technological domains. This paper presents a simple model that provides an explanatory foundation for these phenomena based upon the inventive design process. The model assumes that invention - novel and useful design- arises through probabilistic analogical transfers that combine existing knowledge by combining existing individual op...

One new thing often leads to another. Such correlated novelties are a familiar part of daily life. They are also thought to be fundamental to the evolution of biological systems, human society, and technology. By opening new possibilities, one novelty can pave the way for others in a process that Kauffman has called "expanding the adjacent possible". The dynamics of correlated novelties, however, have yet to be quantified empirically or modeled mathematically. Here we propose...

Recent advances in the development of artificial intelligence, technological progress acceleration, long-term trends of macroeconomic dynamics increase the relevance of technological singularity hypothesis. In this paper, we build a model of finite-time technological singularity assuming that artificial intelligence will replace humans for artificial intelligence engineers after some point in time when it is developed enough. This model implies the following: let A be the lev...

This paper reports results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From data on more than 2 million patents and their citations, we extract an attractiveness function, $A(k,l)$, which determines the likelihood that a patent will be cited. $A(k,l)$ is approximately separable into a product of a function $A_k(k)$ and a function $A_l(l)$, where...

Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical thermodynamics. In particular we can demonstrate the existence of several distinct phases of evolutionary dynamics: a phase of fast growing diversity, one of stationary, finite diversity, and one of rapidly decaying diversity. While the first two pha...

We study a simple model for the evolution of the cost (or more generally the performance) of a technology or production process. The technology can be decomposed into $n$ components, each of which interacts with a cluster of $d-1$ other, dependent components. Innovation occurs through a series of trial-and-error events, each of which consists of randomly changing the cost of each component in a cluster, and accepting the changes only if the total cost of the entire cluster is...

The web of relations linking technological innovation can be fairly described in terms of patent citations. The resulting patent citation network provides a picture of the large-scale organization of innovations and its time evolution. Here we study the patterns of change of patents registered by the US Patent and Trademark Office (USPTO). We show that the scaling behavior exhibited by this network is consistent with a preferential attachment mechanism together with a Weibull...