DominantStrategy 2002-07-24 00:19:46 2002-07-24 03:54:52 Definition weakly dominant strategy dominates weakly dominates strongly dominates dominant strongly dominant % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here For any player $i$, a strategy $s^*\in S_i$ \emph{weakly dominates} another strategy $s^\prime\in S_i$ if: \begin{displaymath} \forall s_{-i}\in S_{-i}\left[u_i(s^*,s_{-i})\geq u_i(s^\prime,s_{-i})\right] \end{displaymath} (Remember that $S_{-i}$ represents the product of all strategy sets other than $i$'s) $s^*$ \emph{strongly dominates} $s^\prime$ if: \begin{displaymath} \forall s_{-i}\in S_{-i}\left[u_i(s^*,s_{-i})> u_i(s^\prime,s_{-i})\right] \end{displaymath}