The paper presents the existence and uniqueness of equilibrium points in concave n-person games. It defines a concave game as one where each player's payoff function is concave in their own strategy. The paper proves that for strictly concave games, there exists a unique equilibrium point. A dynamic model is proposed, consisting of a system of differential equations that describe how players adjust their strategies to maximize their payoffs. It is shown that this system is globally asymptotically stable, meaning that any initial strategy will converge to the unique equilibrium point. The paper also discusses how gradient methods can be used to find the equilibrium point for a concave game. The results are applied to various cases, including bimatrix games and general n-person games. The paper concludes that the unique equilibrium point of a concave game is globally asymptotically stable, and that gradient methods can be used to find this point. The paper also provides a sufficient condition for diagonal strict concavity, which is necessary for the uniqueness of the equilibrium point. The paper is supported by references to previous work in game theory and optimization.The paper presents the existence and uniqueness of equilibrium points in concave n-person games. It defines a concave game as one where each player's payoff function is concave in their own strategy. The paper proves that for strictly concave games, there exists a unique equilibrium point. A dynamic model is proposed, consisting of a system of differential equations that describe how players adjust their strategies to maximize their payoffs. It is shown that this system is globally asymptotically stable, meaning that any initial strategy will converge to the unique equilibrium point. The paper also discusses how gradient methods can be used to find the equilibrium point for a concave game. The results are applied to various cases, including bimatrix games and general n-person games. The paper concludes that the unique equilibrium point of a concave game is globally asymptotically stable, and that gradient methods can be used to find this point. The paper also provides a sufficient condition for diagonal strict concavity, which is necessary for the uniqueness of the equilibrium point. The paper is supported by references to previous work in game theory and optimization.