dominant strategy

For any player $i$ , a strategy $s^{*}\in S_{i}$ weakly dominates another strategy $s^{\prime}\in S_{i}$ if:

$\forall s_{-i}\in S_{-i}\left[u_{i}(s^{*},s_{-i})\geq u_{i}(s^{\prime},s_{-i})\right]$

(Remember that $S_{-i}$ represents the product of all strategy sets other than $i$ ’s)

$s^{*}$ strongly dominates $s^{\prime}$ if:

$\forall s_{-i}\in S_{-i}\left[u_{i}(s^{*},s_{-i})>u_{i}(s^{\prime},s_{-i})\right]$