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Jan 18, 2011

Jan 18, 2011 - Lecture 4 Dominance Solubility weakly...

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Unformatted text preview: January 18, 2011 - Lecture 4 Dominance Solubility weakly dominated strategy: when the " " " payoffs of a strategy are equal to or lower " " " " " " than those of the other strategies " " " " " " strongly dominated strategy: when the " " strategy are equal to or" " " payoffs of a " " " " " greater than those of the other strategies " " " " " " Left Right Player 2 North South " " " " " (a, b) (e, f) (c, d) (g, h) Player 1 " " 1) Player 1ʼs Left is better than right; a ≥ e and c ≥ g, with at least one equality being strict 2) Player 2, South weakly dominates North d ≥ b and h ≥ f, with at least one being strict (≥) 3) if strongly dominates; d > b and h > f " " " " " " " X Player 2 A B C (1, ) (0, ) (2, ) (2, ) (0, ) (1, ) (2, ) (3, ) (1, ) " " Player 1 " Y " " Z ** for Player 1, Y strictly dominates X ** Iterated Elimination of Weakly Dominated Strategies" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " Up Player 2 Left" Right ** for P1, Up and Middle weakly dominate down " " " " " " " ** for P2, " " Left and Right donʼt dominate each " " " " " " "by crossing out Down, Left "weakly " " " " other, but dominates Right " " " " " The" number in blue "show the order of the elimination " " " " " " " (1, 1) (0, 2) "(0, " " (0, 1) (1, 0) " (0, 0) 2. 1. Player 1 Middle " " " " " 3. Down" " " -1) " " " " " ...
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