MFG / Center Lagrange: The development of MFG methods for the analysis of situations in the presence of partial information

Scientific project

The Institut Louis Bachelier is committed, within the framework of agreements with its clients, to contribute to fundamental exploratory and collaborative research, with the objective that this research draws avenues of scientific work in the perspective of the creation of a new Institute for fundamental and applied research in mathematics oriented towards fields likely to advance fundamental mathematical knowledge likely to have an impact in new information and communications technologies (NICT).

Fundamental research on MFG methods in the presence of partial information, situations that are encountered in particular when agents wish to maintain a certain level of data confidentiality, naturally fits into this context.

In this context, many questions arise. One of the main challenges is to develop robust methods to take into account the global nature of the situations encountered in networks comprising a large number of agents who cannot or do not want to exchange all the information at their disposal. To make a complete analysis of such a system, it will be necessary to go through the development of new theoretical methods making it possible to take into account this absence of perfect information.

Several avenues open up, such as Bayesian techniques and reinforcement learning. The extension of these results to MFG game theory is fundamental in order to take into account the reality of the information available when the number of agents becomes very large.

The IEF as a Research Foundation, provides the appropriate and necessary framework for fundamental research with the objective of advancing scientific knowledge, and has the capacity and attractiveness necessary to mobilize advanced academic skills of the highest level. necessary for this fundamental research leading to scientific publications.

The ILB therefore wishes to entrust a research mission to the IEF on “the development of MFG methods for the analysis of situations in the presence of partial information”.

The mission of the IEF is to carry out the research project:

“The development of MFG methods for the analysis of situations in the presence of partial information”; ensure the scientific publication of the results obtained: an article published in a mathematical journal, and send the ILB a research report on the research carried out, the results obtained, the new avenues opened up by this work, the possible consequences and the expected benefits.

The IEF must therefore:

• Bring together the scientific skills likely to carry out this research,
• Pilot the research work program to carry out this project,
• Ensure the achievement of the deliverables indicated above.