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This paper is concerned with two-person mean-field linear-quadratic non-zerosum stochastic differential games in an infinite horizon. Both open-loop andclosed-loop Nash equilibria are introduced. Existence of an open-loop Nashequilibrium is characterized by the solvability of a system of mean-fieldforward-backward stochastic differential equations in an infinite horizon andthe convexity of the cost functionals, and the closed-loop representation of anopen-loop Nash equilibrium is given through the solution to a system of twocoupled non-symmetric algebraic Riccati equations. The existence of aclosed-loop Nash equilibrium is characterized by the solvability of a system oftwo coupled symmetric algebraic Riccati equations. Two-person mean-fieldlinear-quadratic zero-sum stochastic differential games in an infinite timehorizon are also considered. Both the existence of open-loop and closed-loopsaddle points are characterized by the solvability of a system of two coupledgeneralized algebraic Riccati equations with static stabilizing solutions.Mean-field linear-quadratic stochastic optimal control problems in an infinitehorizon are discussed as well, for which it is proved that the open-loopsolvability and closed-loop solvability are equivalent.

Mean-Field Linear-Quadratic Stochastic Differential Games in an Infinite Horizon