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: $\forall s_{j}\neq s_{i}\in \mathbb {\mathcal {S}} :\quad U(s_{i},s_{-i})\geq U(s_{j},s_{-i})$