Pareto dominant

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

$$\forall i\le n[u_i(s^{*})>u_i(s^{\prime })]$$

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

$$\forall i\le n[u_i(s^{*})\ge u_i(s^{\prime })]$$

$s^{*}$ is strongly Pareto optimal if whenever $s^{\prime }$ weakly Pareto dominates $s^{*}$, $\forall i\le n[u_i(s^{*})=u_i(s^{\prime })]$. 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