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A Mean Field Game Approach for Modelling and Control of Large-Scale Multi-Agent Systems

  • Full or part time
  • Application Deadline
    Monday, April 01, 2019
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description

The modelling and regulation of large-scale multi-agent systems [1] remains an open problem in many diverse research areas such as economics, crowd dynamics and power grids. It has become of crucial importance to properly characterize and control complex systems where a large population of intelligent agents operate independently and pursue their own individual objectives.

From an AI perspective, effective modelling and coordination of these multi-agent systems open up unexplored possibilities in supporting (and potentially replacing) human decision making. In the near future, large numbers of devices that are currently operated manually could instead rely on distributed machine decision making to improve their individual efficiency and positively affect the overall system. For example, in power networks, recent technological developments have led to an increasing penetration of new devices, such as domestic batteries and “smart” appliances (e.g. fridges, washing machines, dishwashers). These loads could operate independently in order to fulfil customers’ requirements and, at the same time, support the operation of the electricity grid.

This project aims at analysing multi-agent systems using recent mathematical discoveries and adopting mean field games [2] to i) describe in a compact manner the complex interactions between large numbers of competing homogeneous agents, ii) characterize the agents’ impact on the overall system and iii) design distributed control strategies to properly coordinate the agents’ behaviour. The underlying conceptual idea is to approximate the size of the agents’ population as infinite. This allows us to simplify considerably the analysis of behaviour and interactions: the contribution of the single (small) agent becomes negligible whereas the overall behaviour of the population can be characterized and controlled with a very limited number of parameters and quantities. In mathematical terms, the stable outcome of the agents’ interactions will correspond to the solution of two coupled partial-differential equations.

The main research activities will include:
- A preliminary analysis that adapts game-theoretical concepts to the specific case of large-scale multi-agent systems, evaluating the necessary assumptions and approximations to be performed.

- A modelling activity where relevant engineering problems are formulated under the new mean field paradigm. The initial focus will be on large populations of “smart” appliances operating in future decarbonized power systems.

- Development of numerical methods and integration schemes to efficiently solve the mean field game equations and determine the likely outcome of the formulated problems.

There is significant potential for applications of the proposed research in an engineering context. In the case of distributed power networks with “smart” appliances, the research could provide innovative solutions to increase flexibility on the demand side, shaping domestic power consumption in order to improve network efficiency and facilitate the integration of renewables. Other relevant applications include road traffic networks and wireless communications.

The potential impact in terms of policy and regulation is also substantial. For example, in the case of “smart” appliances, the proposed methodology will allow us to quantify the value of this new technology, determine the most efficient portfolio of new resources to deploy in the future grid and provide useful insights on related communication and market paradigms.

This project is associated with the UKRI CDT in Accountable, Responsible and Transparent AI (ART-AI), which is looking for its first cohort of at least 10 students to start in September 2019. Students will be fully funded for 4 years (stipend, UK/EU tuition fees and research support budget). Further details can be found at:

Desirable qualities in candidates include intellectual curiosity, a strong background in maths and programming experience.

Applicants should hold, or expect to receive, a First Class or good Upper Second Class Honours degree. A master’s level qualification would also be advantageous.

Informal enquiries about the project should be directed to Dr Antonio De Paola on email address .

Enquiries about the application process should be sent to .

Formal applications should be made via the University of Bath’s online application form for a PhD in Computer Science:

Start date: 23 September 2019.

Funding Notes

ART-AI CDT studentships are available on a competition basis for UK and EU students for up to 4 years. Funding will cover UK/EU tuition fees as well as providing maintenance at the UKRI doctoral stipend rate (£15,009 per annum for 2019/20) and a training support fee of £1,000 per annum.

We also welcome all-year-round applications from self-funded candidates and candidates who can source their own funding.


[1] Ferber, J. (1999). Multi-Agent Systems: An Introduction to Distributed Artificial Intelligence. Addison-Wesley Longman Publishing Co., Inc.
[2] Lasry, J.L., Lions, P.L. (2007) Mean field games. Japanese Journal of Mathematics, 2(1):229-260

How good is research at University of Bath in Electrical and Electronic Engineering, Metallurgy and Materials?

FTE Category A staff submitted: 20.50

Research output data provided by the Research Excellence Framework (REF)

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