Abstract
This note establishes that if the face spanned by a strategy block in a finite normal-form game is asymptotically stable under any evolutionary selection dynamic in a wide class, then the block is a game block as defined by Ritzberger et al. (2025). That is, the block respects Nash equilibrium components and the index sum of the components with support in the block equals +1. The result extends Theorem 1 of Demichelis and Ritzberger (2003) from equilibrium components to faces of strategy blocks.