Large systems of interacting individuals are central to countless areas of science; the individuals may be people, computers, animals, or particles, and the large systems may be financial markets, networks, flocks, or fluids. This project is looking at the theory of mean field games (MFG) and how its study of strategic decision making in very large populations of small interacting individuals can be used to improve smart grids and statistical sampling.
Explaining the science
The theory of mean field games (MFGs) was developed independently by mathematicians Jean Michel Lasry and Pierre-Louis Lions and engineers Minyi Huang, Roland P. Malhame, and Peter Caines in 2006.
It deals with the study of strategic decision-making in very large populations of small, randomly interacting agents or ‘players’. It is inspired by mean field theory in physics which looks at the behaviour of systems of large numbers of particles, such as in gases, where individual particles have negligible impact upon the system as a whole, but affect each other.
In MFGs this equates to the decisions each small agent makes depending on the statistical properties of the states and strategies of other players in the ‘game’ they interact with, but having a very small impact on the game’s overall outcome.
This project is developing the application of mean field game theory in different application areas.
The key feature of the smart grids paradigm is that end customers actively participate in the energy market and consequently their strategic behaviour needs to be analysed (see e.g. Bagagiolo and Bauso, 2014).
Diffusion processes are at the core of many algorithms used in statistics to sample with so-called 'intractable distributions.'