J. B. Rosen proved that in concave games of n players (which assumes that Cartesian product of strategy profiles is convex) if the game satisfies the condition of diagonally strictly concave then there is a unique Nash equilibrium (see here).
Suppose that all users follow gradient descent algorithm (in discrete time space). Suppose that the game satisfies the diagonally strictly concave condition.
Does the strategy profile converge approximately to unique Nash equilibrium (up to some constant depends on the maximal step size)?