This paper introduces a general approach to model games with a large number of players, focusing on Nash equilibria for long-term stochastic problems. As the number of players N tends to infinity, the authors rigorously derive "mean field" type equations. They prove general uniqueness results and determine the deterministic limit. The system of equations involves a Hamiltonian and an operator satisfying specific conditions. In the case where the Hamiltonian is quadratic, the system reduces to the classical Hartree equation in Quantum Mechanics. The paper also discusses various extensions and variants of the model. The authors show that when the number of players tends to infinity, the complexity of the Nash equilibria is significantly simplified. The mean field approach is linked to statistical physics and the study of systems with a large number of particles. The mathematical framework corresponds to well-posed systems of partial differential equations coupling Hamilton-Jacobi-Bellman and Kolmogorov-type equations. The paper also discusses the deterministic limit and the uniqueness of solutions under certain conditions. The results are supported by rigorous mathematical proofs and examples. The authors conclude that the mean field approach provides a powerful tool for analyzing large-scale games and economic systems.This paper introduces a general approach to model games with a large number of players, focusing on Nash equilibria for long-term stochastic problems. As the number of players N tends to infinity, the authors rigorously derive "mean field" type equations. They prove general uniqueness results and determine the deterministic limit. The system of equations involves a Hamiltonian and an operator satisfying specific conditions. In the case where the Hamiltonian is quadratic, the system reduces to the classical Hartree equation in Quantum Mechanics. The paper also discusses various extensions and variants of the model. The authors show that when the number of players tends to infinity, the complexity of the Nash equilibria is significantly simplified. The mean field approach is linked to statistical physics and the study of systems with a large number of particles. The mathematical framework corresponds to well-posed systems of partial differential equations coupling Hamilton-Jacobi-Bellman and Kolmogorov-type equations. The paper also discusses the deterministic limit and the uniqueness of solutions under certain conditions. The results are supported by rigorous mathematical proofs and examples. The authors conclude that the mean field approach provides a powerful tool for analyzing large-scale games and economic systems.