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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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 Spring '10
 AsuOzdaglar

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