Deep Backward and Galerkin Methods for the Finite State Master Equation

arXiv:2403.04975v1 Announce Type: cross
Abstract: 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 for stochastic, differential games with finite but large populations of agents. The master equation is a partial differential equation (PDE) whose solution characterizes MFG equilibria for any possible initial distribution. The first method we propose relies on backward induction in a time component while the second method directly tackles …

abstract agents arxiv differential equation equilibria games master math.oc mean network neural network paper solve state stat.ml stochastic type