  In this article, we study the notion of semi-stability and the
Harder-Narasimhan filtration from a game-theoretic point of view. This allows
us to provide a unified proof for the existence and uniqueness of the
Harder-Narasimhan filtration in various settings and offer a conceptual
interpretation for semi-stability conditions. As an application, we establish
the existence and uniqueness of a coprimary filtration for modules of finite
type over a commutative Noetherian ring and interpret it as a Harder-Narasimhan
filtration.
