Continuous-Time Mean Field Games with Finite State Space and Common Noise

Abstract We formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states common noise, including rigorous probabilistic construction of the state process existence uniqueness results resulting equilibrium system. The key insight is that we can circumvent master equation reduce to system forward-backward systems (random) ordinary differential equations by conditioning on noise events. In absence our setup reduces Gomes, Mohr Souza (Appl Math Optim 68(1): 99–143, 2013) Cecchin Fischer 81(2):253–300, 2020).