# 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:

 $\forall s_{-i}\in S_{-i}\left[u_{i}(s^{*},s_{-i})>u_{i}(s^{\prime},s_{-i})\right]$
 Title dominant strategy Canonical name DominantStrategy Date of creation 2013-03-22 12:51:39 Last modified on 2013-03-22 12:51:39 Owner Henry (455) Last modified by Henry (455) Numerical id 5 Author Henry (455) Entry type Definition Classification msc 91A10 Defines weakly dominant strategy Defines dominates Defines weakly dominates Defines strongly dominates Defines dominant Defines strongly dominant