# Advanced Microeconomics/Dominance and Iterative Deletion

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## Dominance

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