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# No player should play a strictly dominated strategy

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Unformatted text preview: if there exists some si� ∈ Si such that ui (si� , s−i ) > ui (si , s−i ) for all s−i ∈ S−i . 18 Game Theory: Lecture 2 Dominant Strategies Dominated Strategies Deﬁnition (Weakly Dominated Strategy) A strategy si ∈ Si is weakly dominated for player i if there exists some si� ∈ Si such that ui (si� , s−i ) ≥ ui (si , s−i ) ui (si� , s−i ) > ui (si , s−i ) for all s−i ∈ S−i , for some s−i ∈ S−i . No player should play a strictly dominated strategy Common knowledge of payoﬀs and rationality results in iterated elimination of strictly dominated strategies 19 Game Theory: Lecture 2 Dominant Strategies Iterated Elimination of Strictly Dominated Strategies Example: Iterated Elimination of Strictly Dominated Strategies. prisoner 1 / prisoner 2 Confess Don’t confess Suicide Confess (−2, −2) (0, −3) (−2, −10) Don’t confess (−3, 0) (−1, −1) (0, −10) Suicide (−10, −2) (−10, 0) (−10, −10) No dominant strategy equilibrium; because of the additional “suicide” strategy, which is a strictly dominate...
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