lecture2 notes

# Lecture2 notes

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Unformatted text preview: −1 . 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.

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