  In this paper, we consider concave continuous-kernel games characterized by
monotonicity properties and propose discounted mirror descent-type dynamics. We
introduce two classes of dynamics whereby the associated mirror map is
constructed based on a strongly convex or a Legendre regularizer. Depending on
the properties of the regularizer we show that these new dynamics can converge
asymptotically in concave games with monotone (negative) pseudo-gradient.
Furthermore, we show that when the regularizer enjoys strong convexity, the
resulting dynamics can converge even in games with hypo-monotone (negative)
pseudo-gradient, which corresponds to a shortage of monotonicity.
