This paper introduces a general approach to modeling games with a large number of players, focusing on Nash equilibria for long-term stochastic problems. The authors rigorously derive "mean field" equations as the number of players \( N \) approaches infinity. They also prove general uniqueness results and determine the deterministic limit. The system of mean field type equations is derived, involving functions \( v \) and \( m \) that satisfy specific partial differential equations. The paper discusses various extensions and variants, including the case where the Hamiltonian \( H(x, p) \) is a quadratic form, which reduces to the classical Hartree equation in quantum mechanics. The authors demonstrate that solutions are unique if the operator \( \mathcal{V} \) is strictly monotone. Finally, they provide explicit solutions in the deterministic case by letting \( v \) approach zero. The paper highlights the importance of this approach in both game theory and economic modeling, particularly in understanding the behavior of large economic systems.This paper introduces a general approach to modeling games with a large number of players, focusing on Nash equilibria for long-term stochastic problems. The authors rigorously derive "mean field" equations as the number of players \( N \) approaches infinity. They also prove general uniqueness results and determine the deterministic limit. The system of mean field type equations is derived, involving functions \( v \) and \( m \) that satisfy specific partial differential equations. The paper discusses various extensions and variants, including the case where the Hamiltonian \( H(x, p) \) is a quadratic form, which reduces to the classical Hartree equation in quantum mechanics. The authors demonstrate that solutions are unique if the operator \( \mathcal{V} \) is strictly monotone. Finally, they provide explicit solutions in the deterministic case by letting \( v \) approach zero. The paper highlights the importance of this approach in both game theory and economic modeling, particularly in understanding the behavior of large economic systems.