The Household Behavior Modeling Based on Mean Field Games Approach

Abstract: We present a modification of the Ramsey model that describes the consumer behavior of the households. We assume that the salary of the households is a stochastic process, defined by the stochastic differential equation (SDE). The impact of the large amount of the households can be modelled by a mean field term. This leads to a Kolmogorov–Fokker–Planck equation, evolving forward in time that describes the evolution of the probability density function of the households. Considering a Hamilton–Jacobi–Bellman equation, evolving backwards in time that describes the optimal strategy of the households behavior, we obtain a Mean Field Game problem. We present a self-similar solution of the Hamilton–Jacobi–Bellman equation and introduce the numerical solution of the Kolmogorov–Fokker–Planck equation. © 2021, Pleiades Publishing, Ltd.