  In this paper, we propose a second-order extension of the continuous-time
game-theoretic mirror descent (MD) dynamics, referred to as MD2, which provably
converges to mere (but not necessarily strict) variationally stable states
(VSS) without using common auxiliary techniques such as time-averaging or
discounting. We show that MD2 enjoys no-regret as well as an exponential rate
of convergence towards strong VSS upon a slight modification. MD2 can also be
used to derive many novel continuous-time primal-space dynamics. We then use
stochastic approximation techniques to provide a convergence guarantee of
discrete-time MD2 with noisy observations towards interior mere VSS. Selected
simulations are provided to illustrate our results.
