# Pareto dominant

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

 $\forall i\leq n\left[u_{i}(s^{*})>u_{i}(s^{\prime})\right]$

An outcome $s^{*}$ weakly Pareto dominates $s^{\prime}$ if:

 $\forall i\leq n\left[u_{i}(s^{*})\geq u_{i}(s^{\prime})\right]$

$s^{*}$ is strongly Pareto optimal if whenever $s^{\prime}$ weakly Pareto dominates $s^{*}$, $\forall i\leq n\left[u_{i}(s^{*})=u_{i}(s^{\prime})\right]$. That is, there is no strategy which provides at least as large a payoff to each player and a larger one to at least one. $s^{*}$ is weakly Pareto optimal if there is no $s^{\prime}$ such that $s^{\prime}$ strongly Pareto dominates $s^{*}$.

 Title Pareto dominant Canonical name ParetoDominant Date of creation 2013-03-22 12:51:32 Last modified on 2013-03-22 12:51:32 Owner Henry (455) Last modified by Henry (455) Numerical id 6 Author Henry (455) Entry type Definition Classification msc 91A99 Defines strongly Pareto optimal Defines weakly Pareto optimal Defines strongly Pareto dominates Defines strongly Pareto dominant Defines Pareto dominates Defines Pareto dominant Defines weakly Pareto dominates Defines weakly Pareto dominant