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