This paper revisits the analysis of stable sets in two-player strategic-form games. Our two main contributions are (i) to establish a connection between myopic stable sets and the stable matchings of an auxiliary two-sided matching problem and (ii) to identify a structural property of 2-player games, called “the block partition property,” which helps characterize the strategy profiles that are indirectly dominated by a fixed profile. Our analysis also generalizes and unifies existing results on myopic and farsighted stable sets in 2-player games.