This paper investigates pure strategy sequential equilibria of repeated games with imperfect monitoring. The authors focus on the equilibrium value set and static optimization problems embedded in extremal equilibria. They show that the equilibrium value set can be derived from solutions to static problems, leading to a "bang-bang" property in equilibrium strategies. This simplifies the analysis of equilibria and applies to a broad class of asymmetric games, generalizing earlier work on optimal cartel equilibria. The paper also establishes a strong relationship between the equilibrium value set and the discount factor, and provides an algorithm for computing the value set. Key results include the "factorization" theorem, which shows that the equilibrium value set equals the set of admissible pairs, and the "self-generation" theorem, which demonstrates that bounded self-generating sets are sequential equilibrium values. The paper also proves that efficient sequential equilibria have the property that after every history, the value to players of the remainder of the equilibrium must be an extreme point of the equilibrium value set. The results have important implications for the computation of equilibrium values and the analysis of repeated games.This paper investigates pure strategy sequential equilibria of repeated games with imperfect monitoring. The authors focus on the equilibrium value set and static optimization problems embedded in extremal equilibria. They show that the equilibrium value set can be derived from solutions to static problems, leading to a "bang-bang" property in equilibrium strategies. This simplifies the analysis of equilibria and applies to a broad class of asymmetric games, generalizing earlier work on optimal cartel equilibria. The paper also establishes a strong relationship between the equilibrium value set and the discount factor, and provides an algorithm for computing the value set. Key results include the "factorization" theorem, which shows that the equilibrium value set equals the set of admissible pairs, and the "self-generation" theorem, which demonstrates that bounded self-generating sets are sequential equilibrium values. The paper also proves that efficient sequential equilibria have the property that after every history, the value to players of the remainder of the equilibrium must be an extreme point of the equilibrium value set. The results have important implications for the computation of equilibrium values and the analysis of repeated games.