Mean field portfolio games with consumption

We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved be equivalent BSDE. Our approach, enough cover power, exponential log utilities, relies on martingale optimality principle in Cheridito Hu (Stochast Dyn 11(02n03):283–299, 2011) et al. (Ann Appl Probab 15(3):1691–1712, 2005) dynamic programming Espinosa Touzi (Math Financ 25(2):221–257, 2015) Frei dos Reis Econ 4:161–182, 2011). When parameters do not depend Brownian paths, get unique equilibrium closed form. As byproduct, when all are time-independent, answer question proposed Lacker Soret 14(2):263–281, 2020): strong obtained 2020) essentially bounded space.