Corruption via Mean Field Games

Abstract

A new mathematical model governing the development of a corrupted hierarchy is derived. This model is based on the Mean Field Games theory. A retrospective problem for that model is considered. From the applied standpoint, this problem amounts to figuring out the past activity of the corrupted hierarchy using the present data for this community. Three new Carleman estimates are derived. These estimates lead to H\"older stability estimates and uniqueness results for both that retrospective problem and its generalized version. H\"older stability estimates characterize the dependence of the error in the solution of the retrospective problem from the error in the input data.