Advanced Microeconomics/Dominance and Iterative Deletion

Dominance

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

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