# dominant strategy

For any player $i$, a strategy ${s}^{*}\in {S}_{i}$ *weakly dominates* another strategy ${s}^{\prime}\in {S}_{i}$ if:

$$\forall {s}_{-i}\in {S}_{-i}[{u}_{i}({s}^{*},{s}_{-i})\ge {u}_{i}({s}^{\prime},{s}_{-i})]$$ |

(Remember that ${S}_{-i}$ represents the product of all strategy sets other than $i$’s)

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

$$\forall {s}_{-i}\in {S}_{-i}[{u}_{i}({s}^{*},{s}_{-i})>{u}_{i}({s}^{\prime},{s}_{-i})]$$ |

Title | dominant strategy |

Canonical name | DominantStrategy |

Date of creation | 2013-03-22 12:51:39 |

Last modified on | 2013-03-22 12:51:39 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 5 |

Author | Henry (455) |

Entry type | Definition |

Classification | msc 91A10 |

Defines | weakly dominant strategy |

Defines | dominates |

Defines | weakly dominates |

Defines | strongly dominates |

Defines | dominant |

Defines | strongly dominant |