Survival of the strictest: Stable and unstable equilibria under regularized learning with partial information
Abstract
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-to-day behavior of no-regret learning in games
Keywords
Cite
@article{arxiv.2101.04667,
title = {Survival of the strictest: Stable and unstable equilibria under regularized learning with partial information},
author = {Angeliki Giannou and Emmanouil-Vasileios Vlatakis-Gkaragkounis and Panayotis Mertikopoulos},
journal= {arXiv preprint arXiv:2101.04667},
year = {2021}
}