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Details of Grant 

EPSRC Reference: EP/P01240X/1
Title: Boltzmann-type and mean-field models in socio-economic applications
Principal Investigator: Wolfram, Dr M
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: University of Warwick
Scheme: First Grant - Revised 2009
Starts: 01 March 2017 Ends: 31 October 2019 Value (£): 100,251
EPSRC Research Topic Classifications:
Mathematical Analysis Non-linear Systems Mathematics
Numerical Analysis
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
29 Nov 2016 EPSRC Mathematical Sciences Prioritisation Panel November 2016 Announced
Summary on Grant Application Form
Our interactions and behavioral patterns not only impact our personal environment, but also effect the progress and development of our society. Understanding how the exchange of information and knowledge between individuals impacts the productivity of an economy and which incentives promote life long learning and prolonged productivity is of great importance and has stimulated research in the field of social sciences, economics and more recently applied mathematics.

A main challenge corresponds to the problem of deriving mathematical models for macroscopic quantities, for example the productivity of a society, from microscopic interactions. A related problem was studied by Ludwig Boltzmann, who wanted to describe macroscopic quantities of a gas, such as the pressure or the temperature, based on the microscopic collisions of gas molecules. He proposed that the macroscopic behavior can be deduced by studying the average behavior of the system, laying the foundations for kinetic theory. Similar ideas can be adapted to understand how individual interactions affect the overall behavior of a large group. But human interactions are rather complex, often based on personal preferences and/or rational decisions. Rational decision making corresponds to considering pros and cons, while trying to find the optimal strategy. This problem is well known in mean-field game theory, which studies strategic decision making in large groups of interacting individuals.

In this project we aim to develop mathematical tools to describe and analyse trading mechanisms and their impact on the dynamics of the price, using ideas proposed in the field of kinetic theory. A second goal corresponds to the coupling of kinetic and mean-field game theory to understand how strategic decisions influence the overall behavior of large groups. This approach will be used for example to analyse the effect of knowledge exchange and dissemination on the overall productivity of an economy. The developed techniques and results allow us to identify driving factors for sustained economic growth. As a part of this project we will develop numerical algorithms, which shall support the theoretical results but also give implications about the dynamic behavior in more complex situations.

The research will be carried out at the Mathematics Institute at the University of Warwick by the PI working with collaborators from prestigious overseas and national universities. These experts in the field of nonlinear partial differential equation theory, mathematical finance as well as economics will be actively involved in the project, and will help to develop and disseminate the obtained results.
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Organisation Website: http://www.warwick.ac.uk