Reconstructing a state-independent cost function in a mean-field game model
- Resource Type
- Working Paper
- Authors
- Ren, Kui; Soedjak, Nathan; Wang, Kewei; Zhai, Hongyu
- Source
- Subject
- Mathematics - Analysis of PDEs
Mathematics - Optimization and Control
35Q89, 35R30, 91A16
- Language
In this short note, we consider an inverse problem to a mean-field games system where we are interested in reconstructing the state-independent running cost function from observed value-function data. We provide an elementary proof of a uniqueness result for the inverse problem using the standard multilinearization technique. One of the main features of our work is that we insist that the population distribution be a probability measure, a requirement that is not enforced in some of the existing literature on theoretical inverse mean-field games.