- Strategy z1 weakly dominates strategy z2 for a given player Pj if both 1. choosing z2 never gives a higher utility for Pj than choosing z1 2. there exist strategies for other players such that choosing z1 gives Pj a higher utility than choosing z2 - Strategy z1 strictly dominates strategy z2 for Pj if choosing z1 gives Pj a higher utility than choosing z2 regardless of other players' strategies - T (elling) strictly dominates S(ilent) in the Prisoner's Dilemma Questions: - If one player has a strategy (e.g., z1 ) that strictly dominates all other strategies, can a NE exist in which that player does not play z1 ? - If one player has a strategy (z2) that is strictly dominated by another (e.g., z1), can z2 be part of a NE? - HARDER: If one player has a strategy (z2) that is weakly dominated by another (e.g., z1 ), can z2 be part of a NE? - Strategy z1 weakly dominates strategy z2 for a given player Pj if both 1. choosing z2 never gives a higher utility for Pj than choosing z1 2. there exist strategies for other players such that choosing z1 gives Pj a higher utility than choosing z2 - Strategy z1 strictly dominates strategy z2 for Pj if choosing z1 gives Pj a higher utility than choosing z2 regardless of other players' strategies - T (elling) strictly dominates S(ilent) in the Prisoner's Dilemma Questions: - If one player has a strategy (e.g., z1 ) that strictly dominates all other strategies, can a NE exist in which that player does not play z1 ? - If one player has a strategy (z2) that is strictly dominated by another (e.g., z1), can z2 be part of a NE? - HARDER: If one player has a strategy (z2) that is weakly dominated by another (e.g., z1 ), can z2 be part of a NE