  In this paper, we provide exponential rates of convergence to the interior
Nash equilibrium for continuous-time dual-space game dynamics such as mirror
descent (MD) and actor-critic (AC). We perform our analysis in $N$-player
continuous concave games that satisfy certain monotonicity assumptions while
possibly also admitting potential functions. In the first part of this paper,
we provide a novel relative characterization of monotone games and show that MD
and its discounted version converge with $\mathcal{O}(e^{-\beta t})$ in
relatively strongly and relatively hypo-monotone games, respectively. In the
second part of this paper, we specialize our results to games that admit a
relatively strongly concave potential and show AC converges with
$\mathcal{O}(e^{-\beta t})$. These rates extend their known convergence
conditions. Simulations are performed which empirically back up our results.
