| Version current |
Version 1 |
| For any player $i$, a strategy $s^*\in S_i$ \emph{weakly dominates} another strategy $s^\prime\in S_i$ if: |
For any player $i$, a strategy $s^*\in S_i$ \emph{weakly dominates} another strategy $s^\prime\in S_i$ if: |
| \begin{displaymath} |
\begin{displaymath} |
| \forall s_{-i}\in S_{-i}\left[u_i(s^*,s_{-i})\geq u_i(s^\prime,s_{-i})\right] |
\forall s_{-i}\in S_{-i}\left[u_i(s^*,s_{-i})\geq u_i(s^\prime,s_{-i})\right] |
| \end{displaymath} |
\end{displaymath} |
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| (Remember that $S_{-i}$ represents the product of all strategy sets other than $i$'s) |
(Remember that $S_{-i}$ represents the product of all strategy sets other than $i$'s) |
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| $s^*$ \emph{strongly dominates} $s^\prime$ if: |
$s^*$ \emph{strongly dominates} $s^\prime$ if: |
| \begin{displaymath} |
\begin{displaymath} |
| \forall s_{-i}\in S_{-i}\left[u_i(s^*,s_{-i})> u_i(s^\prime,s_{-i})\right] |
\forall s_{-i}\in S_{-i}\left[u_i(s^*,s_{-i})> u_i(s^\prime,s_{-i})\right] |
| \end{displaymath} |
\end{displaymath} |
