# 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 |