3 papers
math.OC2024
Convergence of the Deep Galerkin Method for Finite State Mean Field Control Problems
William Hofgard, Jingruo Sun, Asaf Cohen
We establish the convergence of the deep Galerkin method (DGM), a deep learning-based scheme for solving high-dimensional nonlinear PDEs, for Hamilton-Jacobi-Bellman (HJB) equation…
math.OC2024
Asymptotic Nash Equilibria of Finite-State Ergodic Markovian Mean Field Games
Asaf Cohen, Ethan Zell
Mean field games (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric -player games. We consider the finite-state, in…
math.OC2024
Deep Backward and Galerkin Methods for the Finite State Master Equation
Asaf Cohen, Mathieu Laurière, Ethan Zell
This paper proposes and analyzes two neural network methods to solve the master equation for finite-state mean field games (MFGs). Solving MFGs provides approximate Nash equilibria…