Advanced Microeconomics/Dominance and Iterative Deletion

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