Abstarct: Consider a situation with n agents or plaxyers where some of the plaxyers form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not (losing). The dimension of a simple game is the smallest positive integer d such that the simple game can be expressed as the intersection of d threshold functions where each threshold function uses a threshold and n weights. In this thesis, we study the lower and upper bounds for the dimension of a simple game. In this regard, the upper bound by Taylor and Zwicker will be presented which states that the dimension is at most the number of maximal losing coalitions then this bound will be significantly improved to the cardinality of a binary covering code with length n and radius 1. As another topic studied in this thesis, we explore the Hat Game. Using covering codes, some optimal strategies for Hat Game will be introduced in both symmetric and asymmetric cases.