Survival of the strictest: Stable and unstable equilibria under regularized learning with partial information

Angeliki Giannou (1) , Emmanouil Vasileios Vlatakis-Gkaragkounis (2) , Panayotis Mertikopoulos (3)

1 NTUA - National Technical University of Athens [Athens]
2 Columbia University [New York]
3 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems

In this paper, we examine the Nash equilibrium convergence properties of no-regret learning in general N-player games. For concreteness, we focus on the archetypal "follow the regularized leader" (FTRL) family of algorithms, and we consider the full spectrum of uncertainty that the players may encounter-from noisy, oracle-based feedback, to bandit, payoff-based information. In this general context, we establish a comprehensive equivalence between the stability of a Nash equilibrium and its support: a Nash equilibrium is stable and attracting with arbitrarily high probability if and only if it is strict (i.e., each equilibrium strategy has a unique best response). This equivalence extends existing continuous-time versions of the "folk theorem" of evolutionary game theory to a bona fide algorithmic learning setting, and it provides a clear refinement criterion for the prediction of the day-today behavior of no-regret learning in games.

Domaines: Optimisation et contrôle [math.OC]

Angeliki Giannou, Emmanouil Vasileios Vlatakis-Gkaragkounis, Panayotis Mertikopoulos. Survival of the strictest: Stable and unstable equilibria under regularized learning with partial information. COLT 2021 - 34th Annual Conference on Learning Theory, Aug 2021, Boulder, United States. pp.1-30. ⟨hal-03342404⟩