MFG / Center Lagrange: The mathematical analysis of EDP MFG systems for the modeling of highly distributed very high density intercommunication networks

Scientific project

The ILB is committed, within the framework of agreements with its clients, to contribute to fundamental exploratory and collaborative research, with the objective that this research will outline scientific work paths with a view to the creation of a new Institute for fundamental research in applied mathematics focused on fields likely to advance mathematical knowledge having an impact in new information and communications technologies (NTIC).

Fundamental research for MFG methods for high-density distributed systems, particularly found in the Internet of Things, fits naturally in this context.

More particularly, it is hoped that fundamental research will make it possible to improve the understanding, mastery and resolution of systems of MFG equations linked to certain problems posed by the modeling of distributed communication networks at high density of connected objects, and more precisely: problems of stochastic homogenization on the one hand; problematic of the existence of incomplete information equilibria on the other hand.

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 the advanced university skills of the highest scientific level necessary for this fundamental research leading to scientific work.

The ILB therefore wishes to entrust a research mission to the IEF on “the mathematical analysis of EDP MFG systems for the modeling of highly distributed intercommunication networks at very high density, within the framework of the stochastic homogenization of ‘on the one hand, incomplete information structures on the other’.

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

“Mathematical analysis of EDP MFG systems for the modeling of highly distributed very high density intercommunication networks, within the framework of stochastic homogenization on the one hand, and incomplete information structures on the other hand”; ensure the scientific publication of the results obtained: two articles published in mathematics journals (one for each sub-topic), and send to the ILB a research report on the research carried out, the results obtained , the possible consequences and the expected repercussions.

The IEF must therefore:

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