B. Duvocelle, P. Mertikopoulos, M. Staudigl, and D. Vermeulen. Mathematics of Operations Research, forthcoming.
In this paper, we examine the long-run behavior of multi-agent online learning in games that evolve over time. Specifically, we focus on a wide class of policies based on mirror descent, and we show that the induced sequence of play (a) converges to Nash equilibrium in time-varying games that stabilize in the long run to a strictly monotone limit; and (b) it stays asymptotically close to the evolving equilibrium of the sequence of stage games (assuming they are strongly monotone). Our results apply to both gradient-based and payoff-based feedback – i.e., when players only get to observe the payoffs of their chosen actions.
arXiv link: https://arxiv.org/abs/1809.03066