A strategy $s_i$ is strictly dominant iff: $\forall s_j \neq s_i \in \mathbb{\mathcal{S}}:\quad U(s_i,s_{-i})>U(s_j,s_{-i})$ A strategy $s_i$ is weakly dominant iff: $\forall s_j \neq s_i \in \mathbb{\mathcal{S}}:\quad U(s_i,s_{-i})\geq U(s_j,s_{-i})$