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i
Step ∞: Deﬁne, for each i ,
∞
Si∞ = ∩k =0 Sik .
21 Game Theory: Lecture 2 Dominant Strategies Iterated Elimination of Strictly Dominated Strategies
(continued)
Theorem
Suppose that either (1) each Si is ﬁnite, or (2) each ui (si , s−i ) is
continuous and each Si is compact (i.e., closed and bounded). Then Si∞
(for each i ) is nonempty.
Proof for part (1) is trivial.
Proof for part (2) in homework.
Remarks:
Note that Si∞ need not be a singleton. Order in which strategies eliminated does not aﬀect the set of strategies that survive iterated elimination of strictly dominated strategies (or iterated strict dominance): also in the homework. 22 Game Theory: Lecture 2 Dominant Strategies How Reasonable is Dominance Solvability
At some level, it seems very compelling. But consider the k  beauty
game.
Each of you will pick an integer between 0 and 100.
The person who was closest to k times the average of the group will
win a prize.
How will you play this game? And why? 23 Game Theory: Lecture 2 Dominant Strategies Revisiting Cournot Competition
Apply iterated strict dominance to Cournot model to predict the
outcome
s2 s2 1 1 B1(s2) B1(s2)
1/2 1/...
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This document was uploaded on 03/19/2014 for the course EECS 6.254 at MIT.
 Spring '10
 AsuOzdaglar

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