Noise through an Additional Variable for Mean Field Games Master Equation on Finite State Space
Abstract
Abstract. This paper provides a mathematical study of the well-posedness of a master equation with terms modeling common noise on finite state space. In this setting, the solution of the master equation depends on an additional variable modeling the value of a stochastic process impacting all players. Using techniques from viscosity solutions, we give sufficient conditions for the existence of a Lipschitz continuous solution on any time interval. Under some structural assumptions, we are even able to treat cases in which the dynamics of this stochastic process depend on the state of the game.
Fields of Study & Subjects
Stochastic processes and financial applications
Complex Systems and Time Series Analysis
Game Theory and Applications
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 58
- Issue
- 4
- Pages
- 4344–4381
- Publication date
- 24 August 2026
- Language
- EN