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). Basic research on new MFG formulations, paving the way for applications in distributed telecommunications systems or in the study of certain financial markets, fits naturally in this context.
In this context, many questions arise. One of the main challenges is to define a general framework of MFG formulation within which the multitude of different current formulations can fit. The game structures studied are more and more numerous and without unification the risk will be of having to develop the same tools in several settings, which will not be necessary in the case where a more general model is established. If formulating such a model proves impossible, understanding the reasons for this impossibility will also be a big step forward.
On the other hand, the class of equations called the master equation, which seems to allow obtaining very general results, suffers from a lack of theoretical result. The identification of general hypotheses under which these equations are well posed will allow a better understanding of many research questions within the framework of the “Lagrange center” project.
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 the 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 new MFG formulations with a view to the generalization of the hypotheses and results encountered in the various current formulations”.
“The new MFG formulations with a view to generalizing the hypotheses and results encountered in the various current formulations”; 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: