Strategic stability under regularized learning in games

In this paper, we examine the long-run behavior of regularized, no-regret learning in1 finite games. A well-known result in the field states that the empirical frequencies2 of no-regret play converge to the game's set of coarse correlated equilibria; however,3 our understanding of how the players' actual strategies evolve over time is much4 more limited - and, in many cases, non-existent. This issue is exacerbated by5 a series of recent results showing that only strict Nash equilibria are stable and6 attracting under regularized learning, thus making the relation between learning7 and pointwise solution concepts particularly elusive. In lieu of this, we take a more8 general approach and instead seek to characterize the setwise rationality properties9 of the players' day-to-day play. To that end, we focus on one of the most stringent10 criteria of setwise strategic stability, namely that any unilateral deviation from the11 set in question incurs a cost to the deviator - a property known as closedness under12 better replies (club).