[J40] - Multi-agent online learning in time-varying games

B. Duvocelle, P. Mertikopoulos, M. Staudigl, and D. Vermeulen. Mathematics of Operations Research, vol. 48, no. 2, pp. 914-941, May 2023.


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

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