Using mathematics to better understand co-evolving networked systems and innovation
The aim is to develop a novel approach to improve our understanding of co-evolving networked systems, modelled in mathematically precise terms and applied to empirical data sets.
We will explore how such mathematical models can illuminate processes of cumulative innovation within different institutional settings. To test competing theoretical accounts, we will also develop statistical methods that can be used to investigate empirical data.
Delivering a toolset for evaluating policy interventions and private initiatives
By studying how policymakers can intervene in complex social and economic dynamics, our research aims to provide tools for evaluating policy interventions and private initiatives. We will use a series of empirical case studies to develop and test the toolset.
The project will focus on public policies aimed at enhancing the self-reinforcing dynamics of social and economic development. We also seek to understand the role of corporations and other actors as they intervene in these socio-economic transformations.
The dynamics of co-evolution
Jain and Krishna (2003) provided our theoretical starting point. They are interested in the dynamics of co-evolution and use network theory to explore autocatalytic sets (ACS) which are sets of simple molecular organisms that are unable to self-replicate, but each providing a catalyst for its fellows.
Likewise, insects and flowering plants have co-evolved, thriving disproportionately by virtue of their mutual adaptations. Jain and Krishna use computational models to simulate such a dynamic system. This reveals ‘punctuated equilibria’, with processes of growth and then partial collapse.
Two evolutionary scales: the fast and slow dynamics
One interesting feature of the Jain and Krishna model is the two evolutionary scales. The fast (or short) dynamics correspond to the fitness propagation within the network, and the slow (or long) dynamics correspond to the update of the network. These features have interpretations in social networks. For example, the fast and slow dynamics can be interpreted respectively as local innovation (transfer of knowledge between similar technologies) and global innovation (updates to the global technology system).
Studying self-reinforcing processes of social and economic change
The two evolutionary scales provide our distinctive focus and vantage point, for studying self-reinforcing processes of social and economic change. We do so across a range of diverse empirical problems:
- we develop groundbreaking mathematical variations on the basic Jain and Krishna model, appropriate to the various case studies
- we link our empirical data analysis to the theoretical economic and social science literature on cumulative causation and innovation
The Jain and Krishna model has attracted a good amount of attention in the literature on complex network dynamics, and they have themselves discussed its potential application to patterns of technological innovation. Nevertheless this is, to our knowledge, the first and most ambitious attempt to apply their model on a multi-disciplinary basis and with a strong empirical and policy emphasis.
Empirical case studies
Patents: The initial empirical case study is on patents, and we have been given access to the PATSTAT datasets we require. Using the case study of patents as our template, we will extend the research across further social and economic case studies with a view to expanding the mathematical, statistical and empirical scope of the Jain and Krishna model.
Additional case studies are likely to include some of the following:
- Mergers and Acquisitions to track the development and co-evolution of different capabilities in firms
- Financial system to model the co-evolution of risks within connected financial systems
- Welfare regimes to model how institutions concerned with social security, vocational training, employment, etc. co-evolve to produce a number of distinct regimes typical of particular countries
- Developing countries to link science and engineering innovations with the institutional contexts and ‘soft technologies’ of the developing world
- Digital social networks to examine the dynamics of social media, and the insights offered by our modelling for data analytics and digital governance
Research overview, data and papers
We are pleased to make available our research data and first findings on co-evolving systems, technology networks, and innovation patterns.