Corruption via Mean Field Games

Speaker: Dr. Kirill Golubnichiy, Department of Mathematics & Statistics, Texas Tech University

Abstract: A new mathematical model describing the evolution of a corrupted hierarchy is derived. This model is based on mean field games theory. We consider a retrospective (inverse) problem for this model. From an applied standpoint, this problem amounts to reconstructing the past activity of the corrupted hierarchy using present-time data for this community. We derive three new Carleman estimates. These estimates yield Hölder stability and uniqueness results for both the retrospective problem and its generalized version. The Hölder stability estimates characterize how the error in the solution of the retrospective problem depends on the error in the input data.